Stopping circle.py

From Werner KRAUTH

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 random
N_trials = 100000
N = 6
data = [0] * N
for iter in range(N_trials):
    NotVisited = set([k for k in range(N)])
    x = 0
    if random.uniform(0.0, 1.0) < 1.0 / N:
        data[x] += 1.0 / N_trials
    else:
        NotVisited = set([k for k in range(N)])
        NotVisited.discard(x)
        while len(NotVisited) > 0:
            sigma = random.choice([-1, 1])
            x = (x + sigma) % N
            NotVisited.discard(x)
        data[x] += 1.0 / N_trials
print('stopping samples')
for k in range(N):
    print('site = ', k,' probability = ', data[k])

site =  0  probability =  0.1673
site =  1  probability =  0.1671
site =  2  probability =  0.1645
site =  3  probability =  0.1657
site =  4  probability =  0.1656
site =  5  probability =  0.1696