random-walks.sagews

import random
def rw():
    return stats.TimeSeries([random.choice([-1r,1r]) for _ in range(1000)]).sums()
︠24c5241e-7397-4d92-8b2b-29777cf23b2f︠
def f(B, seed=1):
    set_random_seed(seed)
    v = [rw() for i in range(B)]
    g = sum([z.plot(thickness=.3) for z in v])
    show(g)
    s = sum([z.abs().vector()/B for z in v])
    avg = stats.TimeSeries(list(s))
    show(avg.plot() + plot(sqrt(2/pi)*sqrt(x), (0,g.xmax()), color='red', thickness=2))

f(3, 1)

f(10, 1)

f(50, 1)

f(5000, 1)