BegRohu Lectures 2024

From Werner KRAUTH

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	This page is part of my [[BegRohu_Lectures_2024|2024 Beg Rohu Lectures]] on "The second Markov chain revolution" at the [https://www.ipht.fr/Meetings/BegRohu2024/index.html Summer School] "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).		This page is part of my [[BegRohu_Lectures_2024|2024 Beg Rohu Lectures]] on "The second Markov chain revolution" at the [https://www.ipht.fr/Meetings/BegRohu2024/index.html 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 [https://arxiv.org/pdf/cond-mat/9612186 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".	+	A "few" years ago, as if it was yesterday, I taught at the 1996 Beg Rohu Summer School on an [https://arxiv.org/pdf/cond-mat/9612186 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.	+	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==		==List of Python program==
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	[[Diffusion CFTP.py | Diffusion CFTP.py]] x β		[[Diffusion CFTP.py | Diffusion CFTP.py]] x β
-	"x" means that the program comes with some explanatory text, even though this text may not be complete	+	===Lecture 3===
-	"β" means that it has been β tested by students at the 2024 Beg Rohu summer school	+	[[SSEPCompact.py | SSEPCompact.py]] x
-	==References==	+	[[SSEPSteady.py | SSEPSteady.py]]
-	Levin, D. A., Peres, Y. & Wilmer, E. L. Markov Chains and Mixing Times (American Mathematical Society, 2008)	+	[[TASEPCompact.py | TASEPCompact.py]] x
-	Krauth, W., Statistical Mechanics: Algorithms and Computations (Oxford University Press, 2006)	+	[[TASEPSteady.py | TASEPSteady.py]]
		+
		+	[[LiftedTASEPCompact.py | LiftedTASEPCompact.py]] x
		+
		+	[[LiftedTASEPSteady.py | LiftedTASEPSteady.py]]
		+
		+	===Lecture 4===
		+
		+
		+	[[Metropolis_X2X4.py | Metropolis_X2X4.py ]]
		+
		+	[[Factor_Metropolis_X2X4.py | Factor_Metropolis_X2X4.py ]]
		+
		+	[[Factor_Metropolis_X2X4_patch.py | Factor_Metropolis_X2X4_patch.py ]]
		+
		+	[[Lifted_Metropolis_X2X4.py | Lifted_Metropolis_X2X4.py ]]
		+
		+	[[ZigZag_X2X4.py | ZigZag_X2X4.py ]]
		+
		+	[[Factor_ZigZag_X2X4.py | Factor_ZigZag_X2X4.py ]]
		+
		+	[[Bounded_Lifted_Metropolis_X2X4.py | Bounded_Lifted_Metropolis_X2X4.py ]]
		+
		+	[[Bounded_ZigZag_X2X4.py | Bounded_ZigZag_X2X4.py ]]
		+
		+	[[Bounded_Factor_ZigZag_X2X4.py | Bounded_Factor_ZigZag_X2X4.py ]]
		+
		+
		+	===Lecture 5===
		+
		+	[[Stopping_circle.py | Stopping_circle.py ]]
		+
		+	[[SSEP_coupling.py | SSEP_coupling.py ]]
		+
		+	[[SSEP_coupling_FTP.py | SSEP_coupling_FTP.py ]]
		+
		+	[[Ising_coupling.py | Ising_coupling.py ]]
		+
		+	[[Ising_coupling_FTP.py | Ising_coupling_FTP.py ]]
		+
		+	[[Hard_spheres_coupling.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==
-	Wasserman, L., All of Statistics (Springer Verlag, 2004)	+	* 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.	+	See the individual pages of my lectures for a large number of more specific references.

---

Current revision

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.