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From Werner KRAUTH

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		+	==Context==
		+	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).
		+
		+	==Python program==
		+
	import numpy as np		import numpy as np
	import itertools		import itertools

---

Revision as of 15:07, 6 June 2024

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).

Python program

import numpy as np
import itertools
import scipy.linalg as la

def factorial(n):
    return 1 if n == 0 else (0 if n == 0 else factorial(n - 1) * n)

for N in [2, 3, 4, 5, 6, 7]:
    FacN = factorial(N)
    ConfCopy = [0] * N
    print(N, 'N', FacN)
#
#   Setup of transition matrix
#
    P   = np.zeros((FacN, FacN))
    Conf = [k for k in range(N)]
    ConfList = list(itertools.permutations(Conf))
    for Conf in ConfList:
        i = ConfList.index(tuple(Conf))
        ConfCopy[:] = Conf
        a = ConfCopy.pop(0)
        for k in range(N):
            TargetConf = ConfCopy[0:k] + [a] + ConfCopy[k:N - 1]
            j = ConfList.index(tuple(TargetConf))
            P[i][j] = 1.0 / float(N)
    eigvals, eigvecsl, eigvecsr = la.eig(P, left=True)
    eigvals.sort()
    stats = [0] * (N+1)
    for a in eigvals:
        index =  int(N * a.real + 0.5)
        stats[index] += 1
    print(stats)