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Richard S. Ellis, Professor |
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| Personal Webpage |
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| Office | LGRT 1428 | | Phone | (413) 545-3125 | | Fax | (413) 545-1801 | | Email | rsellis <at> math.umass.edu | |
| Mailing Address |
| Department of Mathematics and Statistics |
| Lederle Graduate Research Tower |
| University of Massachusetts |
| Amherst, MA 01003-9305 |
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| Courses |
| Real Analysis I |
| Math 623 (MWF 9:05 - 9:55 am, LGRT 1334) |
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| Introduction to Probability |
| Stat 515H (MWF 11:15 - 12:05 pm, LGRT 123) | | |
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| Education | | Ph.D. | New York University, 1972 |
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| | M.S. | New York University, 1971 |
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| | B.A. | Harvard University, 1969 |
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| Research Interests: Probability and analysis, theory of large deviations |
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Professor Ellis studies the asymptotic behavior of random systems using the theory of large deviations, which focuses on the exponential decay of probabilities in those systems. He has applied the theory to a wide range of problems in which detailed information on rare events is required. These include queueing systems as well as systems arising in statistical mechanics, including spin models and models of coherent structures in turbulence. In recent work he has used the theory of large deviations and the theory of convex functions to understand the equivalence and nonequivalence of the microcanonical, canonical, and generalized canonical ensembles both at the thermodynamic level and at the level of equilibrium macrostates. These ensembles are probability distributions used to describe the behavior of particles in statistical mechanical systems.
Professor Ellis is also an Adjunct Professor in the Department of Judaic and Near Eastern Studies at UMass. His involvement in mathematics, Judaic studies, literature, and Buddhism is detailed on his personal webpage. |
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| Selected Publications |
| R. S. Ellis. Entropy, Large Deviations, and Statistical Mechanics. Springer-Verlag, 1985. Reprinted in the series Classics of Mathematics, 2006. |
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| P. Dupuis and R. S. Ellis. A Weak Convergence Approach to the Theory of Large Deviations. John Wiley & Sons, 1997. |
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| M. Costeniuc, R. S. Ellis, H. Touchette, B. Turkington. The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble. Journal of Statistical Physics 119 (2005), 1283-1329. |
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| R. S. Ellis, R. Jordan, P. Otto, B. Turkington. A statistical approach to the asymptotic behavior of a class of generalized nonlinear Schroedinger equations. Communications in Mathematical Physics 244 (2004), 187-208. |
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| R. S. Ellis, K. Haven, B. Turkington. Large deviation principles and complete equivalence and nonequivalence results for pure and mixed ensembles. Journal of Statistical Physics 101 (2000), 999-1064. |
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| R. S. Ellis. Large deviations for a general class of random vectors. Annals of Probability 12 (1984), 1-12. |
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| Richard S. Ellis and Mark Pinsky. The first and second fluid approximations to the linearized Boltzmann equation and The projection of the Navier-Stokes equations upon the Euler equations. Journal de Mathématiques Pures et Appliquées 54 (1975), 125-156 and 54 (1975), 157-182. |
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