 2015

Large Deviation Analysis of a Droplet Model Having a Poisson
Equilibrium Distribution by Richard S. Ellis and Shlomo
Ta’asan. International Journal of Stochastic Analysis,
Volume 2015 (2015), Article ID 287450, 15 pages,
http://dx.doi.org/10.1155/2015/287450.

Detailed Large Deviation Analysis of a Droplet Model Having a Poisson
Equilibrium Distribution by Richard S. Ellis and Shlomo
Ta’asan. 82page Latex manuscript.

This is an unpublished, companion paper to the paper listed in the preceding item. That paper
omits a number of routine proofs, which are given with full details in
this companion paper. This companion paper also contains additional
background information. It is posted at
http://arxiv.org/abs/1405.5091v4.
 2014

The BoltzmannSanov Large Deviation Principle and
Applications to Statistical Mechanics
by Richard S. Ellis and Shlomo Ta’asan. Unpublished. 48page Latex manuscript.
 2012

Conditional Gaussian Fluctuations and Refined Asymptotics of the Spin
in the PhaseCoexistence Region by Richard S. Ellis and Jingran
Li. Journal of Statistical Physics, Volume 149, pages
803–830 (2012). Proofs of every result in
this paper with complete details are available in the
Ph.D. dissertation of Jingran Li.

Refined Asymptotics of the FiniteSize Magnetization via a New Conditional
Limit Theorem for the Spin by Richard S. Ellis and Jingran
Li. 78page Latex manuscript.
 This unpublished
paper contains details of proofs and calculations omitted
from the paper listed in the preceding item. It is posted at
http://arxiv.org/abs/1205.0970.
 2011

Monte Carlo Methods for Rough Free Energy Landscapes: Population
Annealing and Parallel Tempering by Jonathan Machta and Richard
S. Ellis. Journal of
Statistical Physics, Volume 144, pages 541–553 (2011).
 2010

The Theory of Large
Deviations and Applications to Statistical Mechanics by Richard
S. Ellis. LongRange Interacting Systems: Les Houches 2008 Session XC,
pages 227–277. Edited by T. Dauxois, S. Ruffo, and
L. F. Cugliandolo. Oxford University Press (New York), 2010.
 This article is based on lectures that I gave during Session XC, 4–29
August 2008 at École d'Été de Physique Theorique
in Les Houches, France. An updated version of the lecture notes on
which this paper is based is referenced in the fourth item under 2008.

Asymptotic
Behavior of the FiniteSize Magnetization as a Function of
the Speed of Approach to Criticality by Richard S. Ellis,
Jonathan Machta, and Peter TakHun Otto. Annals of Applied
Probability, Volume 20, Number 6, pages 2118–2161 (2010).
 2008

Asymptotic Behavior
of the Magnetization Near Critical and
Tricritical Points via GinzburgLandau Polynomials
by Richard S. Ellis, Jonathan Machta,
and Peter TakHun Otto.
Journal of Statistical Physics, Volume 133, Number 1,
pages 101–129 (2008).

GinzburgLandau
Polynomials and the Asymptotic Behavior of the Magnetization Near
Critical and Tricritical Points by Richard S. Ellis, Jonathan Machta,
and Peter TakHun Otto. 75page Latex manuscript.
 This unpublished
paper contains details of proofs and calculations omitted
from the paper listed in the preceding bullet. It is posted at
http://arxiv.org/abs/0803.0178.

Global Optimization, the Gaussian Ensemble, and Universal Ensemble
Equivalence by Marius Costeniuc, Richard S. Ellis, Hugo Touchette,
and Bruce Turkington). Geometry, Probability and
Integrable Systems. For Henry McKean's SeventyFifth Birthday. Edited by Mark
Pinsky, Hugo Rossi, and Pierre van Moerbeke. MSRI Publications,
Volume 55, 131–165. Cambridge University Press (New York), 2008.

The Theory of Large
Deviations and Applications to Statistical Mechanics by Richard
S. Ellis. An updated version of the lecture notes for three lectures
given August 58, 2008 at École d'Été de Physique
Theorique in Les Houches, France during the August 2008 summer school
devoted to longrange, interacting systems (123 pages).
 A talk based on chapters 3–5 of
these lecture notes is available online. It is titled “From Large Deviations to
Statistical Mechanics: What Is the Most Likely Way for an Unlikely
Event To Happen?”
 At the end of the talk I give a much
simpler derivation of the canonical ensemble than that given in
chapter 5 of the lecture notes. This simpler derivation is based on
standard ideas in information theory, which were pointed out to me by
Neri Merhav, Department of Electrical Engineering at the Technion –
Israel Institute of Technology in Haifa, Israel.
 2007

Multiple Critical Behavior
of Probabilistic Limit Theorems in the Neighborhood of a Tricritical
Point by Marius Costeniuc, Richard S. Ellis, and Peter TakHun Otto.
Journal of Statistical Physics, Volume 127, Number 3,
495–552 (2007).
 2006

Entropy, Large Deviations, and Statistical Mechanics [Grundlehren der
mathematischen Wissenschaften, Volume 271, 364 pages (1985)],
reprinted by SpringerVerlag in their
Classics in Mathematics series (2006).

Generalized Canonical
Ensembles and Ensemble Equivalence
by Marius Costeniuc, Richard S. Ellis, Hugo Touchette,
and Bruce Turkington. Physical Review E, Volume 73,
026105 (8 pages), (2006).

Metastability within the
Generalized Canonical Ensemble by Hugo Touchette, Marius
Costeniuc, Richard S. Ellis, and Bruce Turkington.
Physica A, Volume 365, 132–137
(2006). Proceedings of the 3rd International
Conference on News, Expectations and Trends in Statistical Physics
(NEXTΣΦ 2005) Held in Kolymbari, Crete,
Greece, 13–18 August 2005.

Nonconcave Entropies from
Generalized Canonical Ensembles by Marius Costeniuc, Richard
S. Ellis, and Hugo Touchette. Physical Review E, Volume 74,
Rapid Communications, 010105(R) (4 pages), (2006).

The Theory of Large Deviations and Applications to Statistical
Mechanics by Richard S. Ellis. Lecture notes for the International
Seminar on Extreme Events in Complex Dynamics, October 23–27,
2006 (115 pages). MaxPlanckInstitut für Physik komplexer
Systeme, Dresden, Germany.
 2005

Analysis of Phase
Transitions in the MeanField BlumeEmeryGriffiths Model by
Richard S. Ellis, Peter Otto, and Hugo Touchette. Annals of Applied
Probability, Volume 15, Number 3, 2203–2254 (2005).

Complete
Analysis of Phase Transitions and Ensemble Equivalence for
the CurieWeissPotts Model
by Marius Costeniuc, Richard S. Ellis, and Hugo Touchette.
Journal of Mathematical Physics,
Volume 46, 063301 (25 pages), (2005).

The Generalized Canonical
Ensemble and Its Universal Equivalence with the Microcanonical
Ensemble by Marius Costeniuc, Richard S. Ellis, Hugo Touchette,
and Bruce Turkington. Journal of Statistical Physics, Volume
119, Numbers 5/6, 1283–1329 (2005).

Nonequivalent Ensembles and
Metastability by Hugo Touchette and
Richard S. Ellis.
Complexity, Metastability and Nonextensivity, 81–87
(2005). Proceedings of the 31st
Workshop of the International School of Solid State Physics Held in Erice,
Sicily, Italy, 20–26 July 2004. Edited by C. Beck, G. Benedek,
A. Rapisarda, and C. Tsallis. World Scientific Publishers (Hackensack, NJ).
 2004

An Introduction to the
Thermodynamic and Macrostate Levels of Nonequivalent Ensembles by
Hugo Touchette, Richard S. Ellis, and Bruce Turkington. Physica
A, Volume 340, pages 138–146 (2004).
Proceedings of the Second Sardinian International Conference on News
and Expectations in Thermostatistics (NEXT 2003) Held in Villasimius
(Cagliari), Sardegna, Italy.

A Statistical Approach to the Asymptotic Behavior of a Class of
Generalized Nonlinear Schrödinger Equations by Richard S. Ellis,
Richard Jordan, Peter Otto, and Bruce Turkington. Communications
in Mathematical Physics, Volume 244, pages 187–208 (2004).

Thermodynamic versus Statistical Nonequivalence of Ensembles for the
MeanField BlumeEmeryGriffiths Model by Richard
S. Ellis, Hugo Touchette, and Bruce Turkington. Physica A,
Volume 335, pages 518–538 (2004).
 2003

Large Deviations for a Random Walk Model with StateDependent Noise
by Michelle Boué, Daniel HernándezHernández,
and Richard S. Ellis.
SIAM Journal on Control and Optimization, Volume 42, Number 3,
810–838 (2003).
 2002

Analysis of Statistical Equilibrium Models of
Geostrophic Turbulence by Richard S. Ellis, Kyle
Haven, and Bruce Turkington. Journal of
Applied Mathematics and Stochastic Analysis, Volume 15,
Number 4, 341–361 (2002).

Nonequivalent Statistical Equilibrium Ensembles and Refined Stability
Theorems for Most Probable Flows by Richard S. Ellis, Kyle
Haven, and Bruce Turkington. Nonlinearity, Volume 15,
239–255 (2002).
 On February 27, 2002, my coauthors and I were informed that this
“article has been selected for inclusion on the
Journal Information Page for
Nonlinearity as a Featured Article. . . . Featured
Articles are chosen by the journal for their high quality and interest
to readers.”
 2000

Derivation of Maximum Entropy Principles in TwoDimensional Turbulence
via Large Deviations by Christopher Boucher, Richard S. Ellis, and
Bruce Turkington.
Journal of Statistical Physics, Volume 98, Numbers 5/6, 1235–1278 (2000).

Entropy as a Measure of Randomness: A Fundamental Concept in the
Mathematical Sciences by Richard S. Ellis. Newsletter, Department of Mathematics &
Statistics, University of Massachusetts Amherst, Volume 15, Academic
Year 1999–2000, pages 5–6.

Large Deviation Principles and Complete Equivalence and Nonequivalence
Results for Pure and Mixed Ensembles by Richard S. Ellis, Kyle
Haven, and Bruce Turkington. Journal of
Statistical Physics, Volume 101, Numbers 5/6, 999–1064
(2000).

Large Deviations for Small Noise Diffusions with Discontinuous
Statistics by Michelle Boué, Paul Dupuis, and Richard S. Ellis.
Probability Theory and Related Fields, Volume 116, Number 1, 125–149 (2000).
 1999

Spatializing Random Measures: Doubly Indexed Processes and the Large
Deviation Principle by Christopher Boucher, Richard S. Ellis,
and Bruce Turkington. Annals of Probability, Volume 27, Number 1,
297–324 (1999).
Erratum, Annals of Probability,
Volume 30, Number 4, 2113 (2002).

The Theory of Large Deviations: From Boltzmann’s 1877 Calculation to
Equilibrium Macrostates in 2D Turbulence by Richard S. Ellis.
Physica D, Volume 133, Numbers 1–4, 106–136 (1999).
 A talk based on this
paper is available online.

This paper was reprinted in Predictability:
Quantifying Uncertainty in Models of Complex Phenomena (Special issue
originating from the 18th Annual International Conference of the
Center for Nonlinear Studies, Los Alamos, NM, May 11–15 1998), 106–136
(1999). Edited by Shiyi Chen, Len Margolin, and David Sharp. Elsevier
(Amsterdam).
 1997

A Weak Convergence Approach to the Theory of Large Deviations
by Paul Dupuis and Richard S. Ellis. Research
monograph. Wiley Series in Probability and
Statistics, 479 pages (1997). John Wiley & Sons (New York).
 1995

Large Deviation Analysis of Queueing Systems by Paul
Dupuis and Richard S. Ellis. Stochastic Networks, 347365.
Edited by F. P. Kelly and R. J. Williams. IMA Volumes in Mathematics and Its Applications,
Volume 71 (1995). SpringerVerlag (New York).

The Large Deviation Principle for a General Class of Queueing Systems,
I by Paul Dupuis and Richard S. Ellis.
Transactions of American Mathematical Society,
Volume 347, Number 8, pages 2689–2751 (1995).

Irina IgnatioukRobert pointed out a gap in our proof of the
large deviation upper bound that appears on page 2730 of this
paper. She gives a correct proof of the large deviation upper
bound in her paper,
“Large
Deviations for Processes with Discontinuous Statistics,”
published in Annals of Probability 33:1479–1508 (2005).
She also proves that for any absolutely continuous
path—not just for piecewise linear paths as in our
paper—the rate function has the form given in equation (4.8)
of our paper.

An Overview of the Theory of Large Deviations
and Applications to Statistical Mechanics by Richard S. Ellis.
Scandinavian Actuarial Journal, Number 1, pages 97–142
(1995).
 My paper was solicited for this special memorial volume
commemorating the centennial of the birth of the Swedish mathematician
Harald Cramér, who was the editor of the journal for many
years.
 1993

The Large Deviation Principle for Measures with Random Weights by
Richard S. Ellis, John Gough, and Joseph V. Pulé.
Reviews in Mathematical Physics
Volume 5, Number 4, pages 659–692 (1993).
 1992

Large Deviations for Markov Processes with Discontinuous Statistics
II: Random Walks by Paul Dupuis and Richard S. Ellis.
Probability Theory and Related
Fields, Volume 91, pages 153–194 (1992).

Limit Theorems
for Maximum Likelihood Estimators in the
CurieWeissPotts Model by Richard S. Ellis and Kongming Wang.
Stochastic Processes and Their Applications, Volume 40,
Number 2, pages 251–288 (1992).

Review of James Bucklew’s book Large
Deviation Techniques in Decision, Simulation, and Estimation
by Richard S. Ellis. Bulletin (New Series) of the American Mathematical Society,
Volume 26, Number 1, pages 160–171 (1992).
 1991

Large Deviations for Markov Processes
with Discontinuous Statistics,
I: General Upper Bounds by Paul Dupuis, Richard S. Ellis, and Alan Weiss.
Annals of Probability, Volume 19, Number 3,
1280–1297 (1991).
 1990

A Unified Approach to Large Deviations for Markov Chains and
Applications to Statistical Mechanics by Richard S. Ellis. Stochastic Processes,
Physics and Geometry—Ascona/Locarno, Switzerland, 4–9 July
1988, 392–433 (1990). Edited by S. Albeverio, G. Casati,
U. Cattaneo, D. Merlini, and R. Moresi. World Scientific Publishers
(Teaneck, NJ).

Limit Theorems for the Empirical Vector of the
CurieWeissPotts Model by Richard S. Ellis and Kongming Wang.
Stochastic Processes and Their Applications, Volume 35, Number 1,
59–79 (1990).
 1989

Uniform Large Deviation Property of the
Empirical Process of a Markov Chain by Richard S. Ellis and Aaron Wyner.
Annals of Probability, Volume 17, Number 3, 1147–1151 (1989).
 1988

Inequalities for Multivariate Compound
Poisson Distributions by Richard S. Ellis. Annals of Probability,
Volume 16, Number 2, 658–661 (1988).

Large Deviations for the Empirical Measure
of a Markov Chain with an Application to the Multivariate Empirical
Measure by Richard S. Ellis. Annals of Probability, Volume 16,
Number 4, 1496–1508 (1988).

Multiple Phase Transitions in the Generalized CurieWeiss Model by
Theodor Eisele and Richard S. Ellis. Journal of Statistical Physics, Volume 52, Numbers
1/2, 161–202 (1988).
 1985

Entropy, Large Deviations, and Statistical Mechanics. Research
monograph. Grundlehren der mathematischen Wissenschaften, Volume 271,
364 pages (1985). SpringerVerlag (New York).

Large Deviations and
Statistical Mechanics by Richard S. Ellis. Particle Systems, Random Media, and Large
Deviations, 101123 (1985). Proceedings of the 1984 AMS Summer
Research Conference
Held at Bowdoin College, Brunswick, Maine, June 24–30, 1984. Edited by Richard
Durrett. Contemporary Mathematics, Volume 41. American
Mathematical Society (Providence).
 1984

Large Deviations for a General Class of Random Vectors
by Richard S. Ellis. Annals of Probability, Volume 12, Number 1, 1–12 (1984).
 1983

Continuous Symmetry Breaking in a Mean Field Model
by Richard S. Ellis and Theodor
Eisele. Journal of Physics A: Mathematical and General, Volume 16,
Number l, 195–199 (1983).

Symmetry Breaking and Random Waves for Magnetic Systems on a Circle
by Richard S. Ellis and Theodor Eisele.
Zeitschrift für Wahrscheinlichkeitstheorie und
verwandte Gebiete, Volume 63, Number 3, 297–348 (1983).
 1982

Asymptotics of Certain Random Fields on a Circle by Richard
S. Ellis and Jay S. Rosen. Proceedings of Colloquium on Random
Fields: Rigorous Results in
Statistical Mechanics and Quantum Field Theory (Esztergom, Hungary,
June 2430, 1979), 279321 (1982). Edited by J. Fritz,
J. L. Lebowitz, and D. Szasz. Seria Colloquia Mathematica Societatis
Janos Bolyai, Volume 27. North Holland (New York).

Laplace’s Method for Gaussian Integrals with an
Application to Statistical Mechanics by Richard S. Ellis and Jay
Rosen. Annals of Probability, Volume 10, Number 1, 47–66 (1982).
Correction: Annals of Probability,
Volume 11, Number 2, 456 (1983).

Asymptotic Analysis of Gaussian Integrals, I: Isolated Minimum Points
by Richard S. Ellis and Jay Rosen.
Transactions of the American Mathematical Society,
Volume 273, Number 2, 447–481 (1982).
 1981

Asymptotic Analysis of Gaussian Integrals, II: Manifold of Minimum
Points by Richard S. Ellis and Jay Rosen.
Communications in Mathematical Physics,
Volume 82, Number 2, 153–181 (1981).

Discussion of Karl F. Freed’s paper “Polymers as SelfAvoiding
Walks” by Richard S. Ellis.
Annals of Probability, Volume 9, Number 4, 551–554 (1981).
 This article was prepared at the
invitation of Associate Editor Thomas G. Kurtz.

The GHS Inequality for a Large External Field by Richard S. Ellis,
Charles Newman, and Michael O'Connell.
Journal of Statistical Physics, Volume 26, Number 1, 37–50 (1981).
 1980

Asymptotic Expansions of Gaussian Integrals by Richard S. Ellis
and Jay Rosen. Bulletin
(New Series) of the American Mathematical Society, Volume 3, Number 1,
705–709 (1980).

Limit Theorems for Sums of Dependent Random Variables
Occurring in Statistical Mechanics, II: Conditioning, Multiple Phases,
and Metastability by Richard S. Ellis, Charles M. Newman, and
Jay S. Rosen.
Zeitschrift für Wahrscheinlichkeitstheorie und
verwandte Gebiete, Volume 51, 153–169 (1980).
 1978

Extensions of the Maximum Principle: Exponential Preservation by the
Heat Equation by Richard S. Ellis and Charles Newman.
Journal of Differential Equations, Volume 30, Number 3,
365–379 (1978).

Fluctuationes in CurieWeiss Exemplis by Richard S. Ellis and Charles Newman.
Mathematical Problems in Theoretical Physics, 313–324
(1978). Proceedings of the International Conference Held in Rome, June
615, 1977. Edited by G. Dell'Antonio, S. Doplicher, and
G. JonaLasinio. Springer Lecture Notes in Physics, Number 80.
SpringerVerlag (Berlin).

Limit Theorems for Sums of Dependent Random Variables
Occurring in Statistical Mechanics by Richard S. Ellis
and Charles M. Newman.
Zeitschrift für Wahrscheinlichkeitstheorie und
verwandte Gebiete, Volume 44, 117–139 (1978).

Necessary and Sufficient Conditions for the GHS Inequality with
Applications to Analysis and Probability
by Richard S. Ellis and Charles Newman.
Transactions of the American Mathematical Society,
Volume 237, 83–99 (March, 1978).

The Statistics of CurieWeiss Models
by Richard S. Ellis and Charles Newman.
Journal of Statistical Physics, Volume 19, Number 2,
149–161 (1978).
 1977

Diffusion Approximation for Transport Processes with Boundary
Conditions by Richard S. Ellis and Walter Rosenkrantz.
Indiana University Mathematics
Journal, Volume 26, Number 6, 1075–1096 (1977).

Monotone Decrease of Characteristic Functions by Richard
S. Ellis.
Journal of Statistical Physics, Volume 16, Number 1,
117–118 (1977).
Correction: Journal of
Statistical Physics, Volume 18, Number 1, 107 (1978).
 1976

The GHS and Other Correlation
Inequalities for a Class of Even Ferromagnets
by Richard S. Ellis, James Monroe, and Charles Newman.
Communications in Mathematical Physics, Volume 46, Number 2,
167–182 (1976).

Quantum Mechanical Soft Springs and
Reverse Correlation Inequalities by Richard S. Ellis and
Charles Newman. Journal of Mathematical Physics, Volume 17,
Number 9, 1682–1683 (1976).

Volume of an NSimplex by Multiple Integration by Richard
S. Ellis.
Elemente der Mathematik, Volume 31, Number 3, 57–59 (1976).
 1975

Aspects of the Krook Model of the Boltzmann Equation.
Indiana University Mathematics Journal, Volume 24, Number 10,
915–923 (1975).

Asymptotic Equivalence of the Linear NavierStokes and Heat Equations
in One Dimension by Richard S. Ellis and Mark Pinsky.
Journal of Differential Equations, Volume 17, Number 2,
406–420 (1975).

Asymptotics and Limit Theorems for the Linearized Boltzmann
Equation by Richard S. Ellis. Probabilistic Methods in Differential
Equations, 143–151 (1975). Proceedings of the Conference Held at
University of Victoria, August 19–20,
1974. Edited by Mark A. Pinsky. Springer Lecture Notes in Mathematics,
Number 451. SpringerVerlag (Berlin).

Concavity of Magnetization for a Class of Even Ferromagnets
by Richard S. Ellis. Bulletin
of the American Mathematical Society, Volume 81, Number 5, 925–929 (1975).

The First and Second Fluid Approximations to the Linearized Boltzmann
Equation by Richard S. Ellis and Mark Pinsky.
Journal de Mathématiques Pures et
Appliquées, Volume 54, Number 2, 125–156 (1975).

The Projection of the NavierStokes Equations upon the Euler Equations
by Richard S. Ellis and Mark Pinsky. Journal de
Mathématiques Pures et
Appliquées,
Volume 54, Number 2, 157–182 (1975).

A Simple Proof of the GHS and Further Inequalities by
Richard S. Ellis and James Monroe.
Communications in Mathematical Physics, Volume 41, Number
1, 33–38 (1975).
 1974

An Application of Stochastic Optimal Control Theory to the Optimal
Rescheduling of Airplanes by Richard S. Ellis and Ray Rishel.
IEEE Transactions on
Automatic Control, Volume AC19, Number 2, 139–142 (1974).

Asymptotic Nonuniqueness of the NavierStokes Equations in Kinetic
Theory by Richard S. Ellis and Mark Pinsky. Bulletin of the American Mathematical
Society, Volume 80, Number 6, 1160–1164 (1974).

The Asymptotic
Behavior of the First Real Eigenvalue of Second
Order Elliptic Operators with a Small Parameter in the Highest
Derivatives, II by Allen Devinatz, Richard S. Ellis, and Avner
Friedman. Indiana
University Mathematics Journal, Volume 23, Number 11, 991–1011 (1974).

ChapmanEnskogHilbert Expansion for the OrnsteinUhlenbeck Process
and the Approximation of Brownian Motion by Richard S. Ellis.
Transactions of the
American Mathematical Society, Volume 199, 65–74
(1974).

Limit Theorems for Random Evolutions with Explicit Error
Estimates by Richard S. Ellis.
Zeitschrift für Wahrscheinlichkeitstheorie und verwandte
Gebiete, Volume 28, Number 3, 249–256 (1974).
 1973

ChapmanEnskogHilbert Expansion for a Markovian model of the
Boltzmann Equation by Richard S. Ellis.
Communications on Pure and Applied Mathematics
Volume 26, Number 3, 327–359 (1973).

Limit Theorems for Model Boltzmann Equations with Several Conserved
Quantities by Richard S. Ellis and Mark Pinsky.
Indiana University Mathematics Journal,
Volume 23, Number 4, 287–307 (1973).
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