Diffusion CFTP.py

From Werner KRAUTH

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		+	This algorithm was presented in my 2024 BegRohu lectures. It illustrates the coupling-from-the-past algorithm of Propp and Wilson (1997).
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	import random		import random
	import matplotlib.pyplot as plt		import matplotlib.pyplot as plt

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Revision as of 12:45, 6 June 2024

This algorithm was presented in my 2024 BegRohu lectures. It illustrates the coupling-from-the-past algorithm of Propp and Wilson (1997).

import random
import matplotlib.pyplot as plt

N = 5
pos = []
for stat in range(100000):
   all_arrows = {}
   time_tot = 0
   while True:
      time_tot -= 1
      arrows = [random.choice([-1, 0, 1]) for i in range(N)]
      if arrows[0] == -1: arrows[0] = 0
      if arrows[N - 1] == 1: arrows[N - 1] = 0
      all_arrows[time_tot] = arrows
      positions=set(range(0, N))
      for t in range(time_tot, 0):
         positions = set([b + all_arrows[t][b] for b in positions])
      if len(positions) == 1: break
   a = positions.pop()
   pos.append(a)
plt.title('Backward coupling: 1-d with walls: position at t=0')
plt.hist(pos, bins=N, range=(-0.5, N - 0.5), density=True)
plt.savefig('backward_position_t0.png')
plt.show()