- Historical papers
- Books
- Surveys and reviews
- Subject pointers

- Biographies
- Workshops and conferences

- Miscellaneous
- Historical snippets

- 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.

- L. Boltzmann's 1877 paper: On the relationship between the second
law of
the mechanical theory of heat and the probability calculus.

In Vol III of Boltzmann's Complete Works at Wien University (see page 164)

English translation (by Joël Le Roux)

Other volumes of Boltzmann's Complete Works

- A. Einstein's 1910 paper: The theory of the opalescence of
homogeneous fluids and liquid mixtures near the critical state. Wiley
| pdf

- O. E. Lanford III, Entropy
and
equilibrium states in
classical statistical mechanics, 1973.

- Y. Oono, Large deviation and statistical physics, 1989.
- R. S. Ellis, An
overview
of the theory of large
deviations and applications to statistical mechanics, 1995.

Taylor & Francis | pdf

- J. T. Lewis and C.-E. Pfister, Thermodynamic probability theory: Some aspects of large deviations, 1995.

- 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

- 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.

- 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.

- Basic introduction to large deviation theory
- J. T. Lewis and R. Russell, An introduction to large deviations for teletraffic engineers, 1996.
- S. R. S. Varadhan, Large deviations and entropy, 2008. Euclid | pdf
- More about the mathematics of large deviation theory
- Chapters I-V of F. den Hollander's book. AMS | Amazon | Google books
- Equilibrium statistical mechanics
- 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
- H. Touchette, The large deviation approach to statistical mechanics, 2009.

- Long range systems
- A. Campa, T. Dauxois and S. Ruffo, Statistical
mechanics and dynamics of solvable models with long-range interactions,
2009.

- Nonequilibrium systems

- H. Touchette, R. J. Harris, Large deviation approach to nonequilibrium systems, 2013.
- H. Touchette, The large deviation approach to statistical mechanics, 2009.
- H. Touchette, lecture notes on dynamical large deviations of Markov processes: arxiv:1705.06492
- 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

- B. Derrida, Non-equilibrium steady states: Fluctuations and large deviations of the density and of the current, 2007.
- L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C.
Landim, Stochastic
interacting particle systems out of equilibrium, 2007.

- L. Bertini et al, Macroscopic fluctuation theory, Rev. Mod. Phys. 2015.

- Multifractals
- G. Zohar, Large deviations formalism for multifractals, 1999.
- D. Veneziano, Large deviations of
multifractal measures, 2002.

- Fluctuation relations
- R. J. Harris, G. M. Schutz, Fluctuation theorems for stochastic dynamics, 2007.
- Random walks in random environments
- Chapter VII of F. den Hollander's book. AMS | Amazon | Google books
- Interacting diffusions (McKean-Vlasov limit)
- Chapter X of F. den Hollander's book. AMS | Amazon | Google books
- Quantum systems
- H. Touchette, Sources on quantum large deviations. pdf
- Large deviation simulations
- Importance sampling on wiki
- Good review of importance sampling methods by Juneja and Shahabuddin

- J. Bucklew, Introduction to Rare Event Simulation, Springer, 2004.

- Lecture notes on basic simulation methods. pdf

- Harald Cramér (1893-1985). Wikipedia | Recollections

- Ludwig E. Boltzmann (1844-1906). Wikipedia | Stanford Encyclopedia of Philosophy
- S. R. Srinivasa Varadhan.

Wikipedia | Abel Prize 2007 | IMS profile | AMS interview | MacTutor biography

Complete works at Celebratio Mathematica

- Oscar E. Lanford III (1940-2013). Wikipedia | In memoriam

- Mark Iosifovich Freidlin. Festschrift
- John T. Lewis (1932-2004). Wikipedia | In memoriam
- Ivan Nikolaevich Sanov (1919-1968). Obituary | russian version | picture
- Mark Kac (1914-1984). wiki
| NAS
Memoir | MacTutor
biography

- Workshop on Large Deviations in Statistical Physics at NITheP Stellenbosch on Nov 3-14 2014

- 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

- 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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