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The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems.
Sur un nouveau théorème limite dans la théorie des probabilités
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Crystal statistics. I. A two-dimensional model with an order-disorder transition
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Quelques propriétés générales de l’intégrale de configuration d’un système de particules avec interaction
L. van Hove · 1949
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Sur l’intégrale de configuration pour les systèmes de particules à une dimension
L. van Hove · 1950
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Fluctuations and irreversible processes
L. Onsager and S. Machlup · 1953
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Saddlepoint approximations in statistics
H. E. Daniels · 1954
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Integral over path formulation of statistical theory of irreversible processes
D. Falkoff · 1956
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Information theory and statistical mechanics
E. T. Jaynes · 1957
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Statistical theory of irrversible processes: Part I. Intergral over fluctuation path formulation
D. Falkoff · 1958
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On the probability of large deviations of random variables
I. N. Sanov · 1961
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Classical statistical mechanics of a system of particles
D. Ruelle · 1963
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The free energy of a macroscopic system
M. E. Fisher · 1964
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A proof that the free energy of a spin system is extensive
R. B. Griffiths · 1964
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Microcanonical ensemble in quantum statistical mechanics
R. B. Griffiths · 1965
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Statistical Mechanics
R. H. Fowler · 1966
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Some asymptotic formulae for Wiener integrals
M. Schilder · 1966
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Asymptotic probabilities and differential equations
S. R. S. Varadhan · 1966
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Statistical Mechanics: Rigorous Results
D. Ruelle · 1969
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An Introduction to Probability Theory and its Applications
W. Feller · 1970
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Convex Analysis
R. T. Rockafellar · 1970
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On small random perturbations of dynamical systems
A. D. Wentzell and M. I. Freidlin · 1970
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Asymptotic equivalence of equilibrium ensembles of classical statistical mechanics
L. Galgani, L. Manzoni, and A. Scotti · 1971
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Rigorous results and theorems
R. B. Griffiths · 1972
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Gibbs measures in ergodic theory
Y. G. Sinai · 1972
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Statistical theory of instabilities in stationary nonequilibrium systems with applications to lasers and nonlinear optics
R. Graham · 1973
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Entropy and equilibrium states in classical statistical mechanics
O. E. Lanford · 1973
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Asymptotic evaluation of certain Markov process expectations for large time. I
M. D. Donsker and S. R. S. Varadhan · 1975
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Asymptotic evaluation of certain Markov process expectations for large time. II
M. D. Donsker and S. R. S. Varadhan · 1975
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Onsager-Machlup function for one dimensional nonlinear diffusion processes
W. Horsthemke and A. Bach · 1975
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A theorem about probabilities of large deviations with an application to queuing theory
D. Plachky and J. Steinebach · 1975
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Asymptotic evaluation of certain Markov process expectations for large time. III
M. D. Donsker and S. R. S. Varadhan · 1976
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Variational principle for non-equilibrium states and the Onsager-Machlup formula
H. Hasegawa · 1976
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On large deviations from the invariant measure
J. Gärtner · 1977
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Advanced Mathematical Methods for Scientists and Engineers
C. M. Bender and S. A. Orszag · 1978
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The Onsager-Machlup function as Lagrangian for the most probable path of a diffusion process
D. Dürr and A. Bach · 1978
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A heuristic approach to the Kolmogorov entropy as a disorder parameter
Y. Oono · 1978
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Large deviations of the sample mean in general vector spaces
R. R. Bahadur and S. L. Zabell · 1979
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Theory of fluctuational transitions between stable states of nonlinear oscillators
M. I. Dykman and M. A. Krivoglaz · 1979
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Statistical mechanics of deterministic chaos: The case of one-dimensional discrete process
T. Kai and K. Tomita · 1980
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Chaos, external noise and Fredholm theory
Y. Oono and Y. Takahashi · 1980
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Symbolic dynamics and hyperbolic dynamic systems
V. M. Alekseev and M. V. Yakobson · 1981
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Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics : I. generalized fluctuation-dissipation theorem
G. N. Bochkov and Yu. E. Kuzovlev · 1981
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Onset of cooperative behavior in nonequilibrium steady states
R. Graham · 1981
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Path integral solutions of stochastic equations for nonlinear irreversible processes: The uniqueness of the thermodynamic lagrangian
K. L. C. Hunt and J. Ross · 1981
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A Laplace approximation for sums of independent random variables
A Martin-Löf · 1982
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Asymptotic evaluation of certain Markov process expectations for large time. IV
M. D. Donsker and S. R. S. Varadhan · 1983
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Dominating points and the asymptotics of large deviations for random walk on ℝ d \mathbb{R}^{d}
P. Ney · 1983
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Large deviations for a general class of random vectors
R. S. Ellis · 1984
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Random Perturbations of Dynamical Systems
M. I. Freidlin and A. D. Wentzell · 1984
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Towards the statistical mechanics of chaos
Y. Takahashi and Y. Oono · 1984
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Convex Analysis: An Introductory Text
J. van Tiel · 1984
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Estimates of quantum deviations from classical mechanics using large deviation results
P. Blanchard, P. Combe, M. Sirugue, and M. Sirugue-Collin · 1985
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Ergodic theory of chaos and strange attractors
J.-P. Eckmann and D. Ruelle · 1985
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Entropy, Large Deviations, and Statistical Mechanics
R. S. Ellis · 1985
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Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences
C. W. Gardiner · 1985
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Weak-noise limit of Fokker-Planck models and nondifferentiable potentials for dissipative dynamical systems
R. Graham and T. Tél · 1985
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Nonequilibrium potential for coexisting attractors
R. Graham and T. Tél · 1986
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Introduction to Path-Integral Methods in Physics and Polymer Science
F. W. Wiegel · 1986
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The theory of opalescence of homogeneous fluids and liquid mixtures near the critical state
A. Einstein · 1987
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Statistical Mechanics
K. Huang · 1987
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Nondifferentiable potentials for nonequilibrium steady states
H. R. Jauslin · 1987
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Activation energy for thermally induced escape from a basin of attraction
R. L. Kautz · 1987
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Markov additive processes I: Eigenvalue properties and limit theorems
P. Ney and E. Nummelin · 1987
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Markov additive processes II: Large deviations
P. Ney and E. Nummelin · 1987
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Anomalous scaling laws in multifractal objects
G. Paladin and A. Vulpiani · 1987
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The free energy of quantum spin systems and large deviations
W. Cegla, J. T. Lewis, and G. A. Raggio · 1988
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Multiple phase transitions in the generalized Curie-Weiss model
T. Eisele and R. S. Ellis · 1988
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Thermally induced escape: The principle of minimum available noise energy
R. L. Kautz · 1988
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Random perturbations of dynamical systems
Y. Kifer · 1988
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The large deviation principle in statistical mechanics
J. T. Lewis · 1988
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The large deviation principle in statistical mechanics: An expository account
J. T. Lewis · 1988
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Large deviations for the empirical field of Curie-Weiss models
S. Orey · 1988
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The large deviation principle and some models of an interacting boson gas
M. van den Berg, J. T. Lewis, and J. V. Pule · 1988
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Asymptotic Techniques for Use in Statistics
O. E. Barndorff-Nielsen and D. R. Cox · 1989
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Instanton calculation of the escape rate for activation over a potential barrier driven by colored noise
A. J. Bray and A. J. McKane · 1989
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Large Deviations
J. D. Deuschel and D. W. Stroock · 1989
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Singular local structures of chaotic attractors and q-phase transitions of spatial scaling structures
H. Hata, T. Horita, H. Mori, T. Morita, and K. Tomita · 1989
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Hydrodynamics and large deviation for simple exclusion processes
C. Kipnis, S. Olla, and S. R. S. Varadhan · 1989
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Large deviations and statistical mechanics
J. T. Lewis · 1989
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Statistical mechanics of dynamical systems
H. Mori, H. Hata, T. Horita, and T. Kobayashi · 1989
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Noise in Nonlinear Dynamical Systems
F. Moss and P. V. E. McClintock, editors · 1989
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Noise in Nonlinear Dynamical Systems
F. Moss and P. V. E. McClintock, editors · 1989
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Large deviation and statistical physics
Y. Oono · 1989
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Asymptotics of Varadhan-type and the Gibbs variational principle
D. Petz, G. A. Raggio, and A. Verbeure · 1989
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The thermodynamic formalism for expanding maps
D. Ruelle · 1989
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Some Markov methods in the theory of stochastic processes in nonlinear dynamical systems
R. L. Stratonovich · 1989
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Path-integral formulation for stochastic processes driven by colored noise
H. S. Wio, P. Colet, M. San Miguel, L. Pesquera, and M. A. Rodríguez · 1989
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Path integrals and non-Markov processes. II. Escape rates and stationary distributions in the weak-noise limit
A. J. Bray, A. J. McKane, and T. J. Newman · 1990
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Large Deviation Techniques in Decision, Simulation and Estimation
J. A. Bucklew · 1990
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Limit theorems for the empirical vector of the Curie-Weiss-Potts model
R. S. Ellis and K. Wang · 1990
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Dissipation and large thermodynamic fluctuations
G. L. Eyink · 1990
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Large deviations in dynamical systems and stochastic processes
Y. Kifer · 1990
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Large deviations from the hydrodynamical limit for a system of independent brownian particles
C. Kipnis and S. Olla · 1990
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Level I theory of large deviations in the ideal gas
T. Lehtonen and E. Nummelin · 1990
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Entropy and large deviation
A. O. Lopes · 1990
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Introduction to multifractals in dynamical systems theory and fully developed fluid turbulence
J. L. McCauley · 1990
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Path integrals and non-Markov processes. I. General formalism
A. J. McKane, H. C. Luckock, and A. J. Bray · 1990
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Linearities of the f ( α ) f(\alpha) spectrum at bifurcations of chaos in dissipative differential systems
H. Tominaga, H. Hata, T. Horita, H. Mori, and K. Tomita · 1990
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Some large deviation results for dynamical systems
L.-S. Young · 1990
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From Microphysics to Macrophysics: Methods and Applications of Statistical Physics
R. Balian · 1991
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Elements of Information Theory
T. M. Cover and J. A. Thomas · 1991
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Statistical Physics
L. D. Landau and E. M. Lifshitz · 1991
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An overview on large deviations of the empirical measure of interacting particle systems
C. Landim · 1991
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Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales
G. M. Wang, E. M. Sevick, E. Mittag, D. J. Searles, and D. J. Evans · 2002
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Large deviations in quantum information theory
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Exact large deviation functional of a stationary open driven diffusive system: The asymmetric exclusion process
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Probability Theory: The Logic of Science
E. T. Jaynes · 2003
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Entropy production fluctuations of finite Markov chains
D.-Q. Jiang, M. Qian, and F.-X. Zhang · 2003
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Negative specific heat of a magnetically self-confined plasma torus
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Large deviations and phase separation in the two-dimensional Ising model
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Large Scale Dynamics of Interacting Particles
H. Spohn · 1991
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Large deviations for exchangeable random vectors
I. H. Dinwoodie and S. L. Zabell · 1992
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Optimal paths and the prehistory problem for large fluctuations in noise-driven systems
M. I. Dykman, P. V. E. McClintock, V. N. Smelyanski, N. D. Stein, and N. G. Stocks · 1992
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Stochastic Processes in Physics and Chemistry
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Thermodynamics of Chaotic Systems: An Introduction
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On the origin and the use of fluctuation relations for the entropy
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Time-reversal and entropy
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Large deviations and a fluctuation symmetry for chaotic homeomorphisms
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Asymptotic properties of stable densities and the asymmetric large deviation problems
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Metastability and entropy
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Work fluctuations, transient violations of the second law and free-energy recovery methods: Perspectives in theory and experiments
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Spin Glasses: A challenge for Mathematicians
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Extension of the fluctuation theorem
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Stationary and transient work-fluctuation theorems for a dragged Brownian particle
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Large deviations and entropy
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