Large deviation theory: History, sources, references, and pointers
Historical papers
Mathematics
- H. Cramér, Sur un nouveau théorème limite dans la théorie des
probabilités, 1938. Google
books
French copy | Side-by-side translation with commentary
- I. N. Sanov, On the probability of large deviations of random
magnitudes, 1957.
Russian original
| English
translation
- S. R. S. Varadhan, Asymptotic
probabilities and differential equations, 1966.
- D. Plachky and J. Steinebach, A theorem about
probabilities of large deviations with an application to queuing theory,
1975.
- M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of
certain Markov process expectations for large time, 1975 and 1976. Part
I | Part
II | Part
III | Part
IV
- J. Gärtner, On large
deviations from the invariant measure, 1977.
- R. R. Bahadur and S. L. Zabell, Large
deviations of the sample mean in general vector spaces, 1979.
JSTOR | Euclid
- A. Martin-Löf, A
Laplace approximation for sums of independent random variables,
1982.
- R. S. Ellis, Large
deviations for a general class of random vectors, 1984. JSTOR | Euclid | pdf
- E. Bolthausen, Laplace
approximations for sums of independent random vectors, 1986.
Physics
Books
- A. Dembo and O. Zeitouni,
Large Deviations
Techniques and Applications, Springer, 1998.
Springer
| Amazon
| Google
books
- F. den Hollander,
Large Deviations, Fields Institute Monograph, AMS,
2000.
AMS
| Amazon
| Google
books
- S. R. S. Varadhan, Large
Deviations and Applications, SIAM, 1984. SIAM | Google
books
- R. S. Ellis, Entropy,
Large Deviations, and
Statistical Mechanics, Springer, 1985. Springer
| Amazon
- J. D. Deuschel and D. W.
Stroock, Large Deviations, Academic Press, 1989. Amazon
| Google
books
- J. Feng and T. G. Kurtz, Large deviations for stochastic
processes, 2005. AMS
| Amazon
- M. I. Freidlin and A. D. Wentzell, Random Perturbations
of Dynamical Systems, Springer, 1984.
Springer
| Amazon
| Google
books
- J. A. Bucklew, Large
Deviation Techniques in
Decision, Simulation and Estimation, Springer, 1990. Springer | Amazon
| Google
books
- A. Shwartz and A. Weiss,
Large Deviations for
Performance Analysis: Queues, Communications, and Computing, CRC, 1995.
CRC
| Amazon
| Google
books
Surveys and reviews
Mathematics
- S. R. S. Varadhan, Large
deviations and entropy, 2008. Euclid | pdf
- S. Ramasubramanian, Large
deviations: An introduction to 2007 Abel prize, 2008.
- J. T. Lewis and R. Russell, An
introduction to large deviations for teletraffic engineers, 1996.
- A.-S. Sznitman, Grandes déviations, 1986. Numdam
| pdf
- A. Amann and H.
Atmanspacher, Introductory
remarks
on large deviation statistics, 1999.
- P. Baldi, An
introduction to the theory of large deviations, 1986.
- R. V. Roy, Noise
perturbations of nonlinear dynamical systems, 1993.
- P. Mörters, Large
deviation theory and applications, 2008.
- S. Robertson and C. Almost, Large
deviation principles, 2010.
- H. Touchette, A basic
introduction to large deviations: Theory,
applications, simulations, 2011.
Physics
- R.
S. Ellis, An
overview
of the theory of large
deviations and applications to statistical mechanics, 1995.
Taylor
& Francis | pdf
- R. S. Ellis, The theory
of
large
deviations: From Boltzmann's 1877 calculation to
equilibrium
macrostates in 2D turbulence, 1999. Physica D
| pdf
- Y. Oono, Large
deviation
and statistical physics, 1989.
- R. S. Ellis, The
theory of large deviations and applications to statistical mechanics,
2008.
- R. Graham, Macroscopic potentials, bifurcations and noise in
dissipative systems, 1989. Springer | CUP
- D. G. Luchinsky, P. V. E. McClintock and M. I. Dykman, Analogue studies of
nonlinear systems, 1998.
- H. Touchette, The large
deviation approach to statistical mechanics, 2009.
Subject pointers
- Basic introduction to large deviation theory
- More about the mathematics of large deviation theory
- Equilibrium statistical mechanics
- Long range systems
- Nonequilibrium systems
- Low-noise limit (Freidlin-Wentzell-Graham theory)
- R. Graham, Macroscopic potentials, bifurcations and noise in
dissipative systems, 1989.
Springer
| CUP
- Interacting particle
systems and macroscopic (or hydrodynamic) fluctuation theory
- Multifractals
- Fluctuation relations
- Random walks in random environments
- Interacting diffusions (McKean-Vlasov limit)
- Quantum systems
- H. Touchette, Sources on quantum large deviations. pdf
- Large deviation simulations
Biographies
Workshops and conferences
Miscellaneous
- Large
deviation theory on Wikipedia
- Convex
analysis on Wikipedia
- Legendre-Fenchel
transform on Wikipedia
- W. Fenchel, On
conjugate convex functions, 1949.
- H. Touchette, Legendre-Fenchel
transforms in a nutshell, 2005.
- H. Touchette, Notes on large
deviations, 2013.
- M. Kac, Petroleum notes on stochastic processes, 1956. pdf
- M. Kac, Pisa Lectures on Integration in Function Spaces and Some
of Its Applications, 1980. pdf
Historical snippets
- Excerpt from Boltzmann's 1877 paper (see link above) showing the entropy M
(more
precisely, minus the entropy), expressed as a function of the
occupation value w_i of the i-th energy level and the two constraints
(number n of particles and energy L) used for maximizing the entropy
(respectively, minimizing M). Boltzmann uses the letter l for the natural logarithm:
- Excerpt from Einstein's 1910 paper (see link above) on
critical opalescence showing his formula for the probability of a
macrostate expressed as the exponential of the entropy:
- Excerpt from Sanov's 1957 paper (see link above) with his main theorem, discovered
by Boltzmann 80 years before!
- Mark Kac in Sec. 9 of his Pisa Lecture Notes, 1980: 'This [...]
section is devoted to a brief introduction to the recent work of
Donsker and Varadhan, which, in my opinion, is the most interesting and
novel development in the field of functional integration since the
ascendency of the subject in the early fifties.'
Google
books | pdf
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