Physics of Complex Systems Master

Stochastic processes
Emmanuel Trizac (LPTMS, Paris-Saclay/CNRS)

Mathematical prerequisites     solution

Lecture Notes

Exercices     solutions ex 1 to 13

1 - Binder cumulants and phase transitions    solution
2 - Gaussian calculus    solution
3 - Primer on random walks, first returns and broad distributions     solution
4 - Large deviations     solution
5 - Discrete random walks    solution
Complement - On the fluctuation relation    solution

2021-2022     solution     feedback
2022-2023     solution     feedback

A good and concise crash course in stat mech is: Introduction to Modern Statistical Mechanics, D. Chandler, Oxford University Press
Mathematics for Physics and Physicists, W. Appel, Princeton University Press, 2007
    also exists in French (éditions H&K)
Physique et outils mathématiques ; méthodes et exemples, A. Alastuey, M. Magro, P. Pujol, Edp Sciences Savoirs Actuels
The Fokker-Planck Equation: Methods of Solutions and Applications, H. Risken, Springer.
Stochastic Processes in physics and chemistry, N. G. van Kampen, Elsevier.
Stochastic Thermodynamics: An Introduction, L. Peliti and S. Pigolotti, Princeton University Press.
Information, Physics, and Computation, M. Mézard and A. Montanari, Oxford University Press
Some useful documents
An elementary RG approach to the generalized central limit theorem, A. Amir, J. Stat. Mech. 013214 (2020)
The tragic life and brilliant legacy of Vincent Doblin/Wolfgang Döblin
Brownian Motion, "Diverse and Undulating" (B. Duplantier)
A simple proof of Perron-Frobenius theorem for symmetric matrices
On the elusive origins of the word 'martingale'

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