BegRohu Lectures 2024
From Werner KRAUTH
Contents |
Context
This page is part of my 2024 Beg Rohu Lectures on "The second Markov chain revolution" at the Summer School "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).
A "few" years ago, as if it was yesterday, I was invited to the 1996 Beg Rohu Summer School, where I gave an Introduction To Monte Carlo Algorithms. The lecture notes of this first course were found readable and the drawings enjoyable, so I made them into a 2006 book for Oxford University Press entitled "Statistical Mechanics: Algorithms and Computations".
The 2024 lectures discuss the foundations of the enormous corpus of works that have constituted the second revolution in Markov chains and Monte Carlo algorithm, namely the understanding of time scales in stochastic dynamics and the concepts of coupling, thinning and, last not least, the systematic construction of non-reversible (that is, non-equilibrium) Markov chains that nevertheless converge to the imposed equilibrium steady state. I hope that what I present here is again found readable and enjoyable, ...
List of Python program
Lecture 1
Bernoulli_two_pebbles_patch.py
Sample_transformation_power.py
Lecture 2
Top_to_random_eigenvalues.py x β
Lecture 3
"x" means that the program comes with some explanatory text, even though this text may not be complete
"β" means that it has been β tested by students at the 2024 Beg Rohu summer school
References
Levin, D. A., Peres, Y. & Wilmer, E. L. Markov Chains and Mixing Times (American Mathematical Society, 2008)
Krauth, W., Statistical Mechanics: Algorithms and Computations (Oxford University Press, 2006)
Wasserman, L., All of Statistics (Springer Verlag, 2004)
More specific references can be found in the individual lectures or with the individual programs.
