BegRohu Lectures 2024

From Werner KRAUTH

Contents 1 Context 2 List of Python program 2.1 Lecture 1 2.2 Lecture 2 2.3 Lecture 3 2.4 Lecture 4 2.5 Lecture 5 3 References

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 taught at the 1996 Beg Rohu Summer School on 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.py

Bernoulli_two_pebbles.py

Bernoulli_two_pebbles_patch.py

Bernoulli_poisson.py

Sample_transformation_exp.py

Sample_transformation_power.py

Buggy_surface_2d.py

Naive_surface_2d.py

Direct_surface_2d.py

Walker.py

Lecture 2

Top_to_random_eigenvalues.py x β

Top to random simul.py

Top_to_random_simul_stop.py

Top-to-random-TVD.py

Top to random TVD mix rel.py

Diffusion.py x

Diffusion_forward.py

Diffusion_CFTP_coupl_pos.py

Diffusion CFTP.py x β

Lecture 3

SSEPCompact.py x

SSEPSteady.py

TASEPCompact.py x

TASEPSteady.py

LiftedTASEPCompact.py x

LiftedTASEPSteady.py

Lecture 4

Metropolis_X2X4.py

Factor_Metropolis_X2X4.py

Factor_Metropolis_X2X4_patch.py

Lifted_Metropolis_X2X4.py

ZigZag_X2X4.py

Factor_ZigZag_X2X4.py

Bounded_Lifted_Metropolis_X2X4.py

Bounded_ZigZag_X2X4.py

Bounded_Factor_ZigZag_X2X4.py

Lecture 5

Stopping_circle.py

SSEP_coupling.py

SSEP_coupling_FTP.py

Ising_coupling.py

Ising_coupling_FTP.py

Hard_spheres_coupling.py

"x" means that the program "already" has some explanatory text, even though this text may not yet 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)

See the individual pages of my lectures for a large number of more specific references.