Consider simple symmetric random walk in two dimensions. This walkstarts at the

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Consider simple symmetric random walk in two dimensions. This walkstarts at the origin and takes successive independent unit stepsNorth, South, East or West, each with probability 1/4. (a) Show that the probability p2n that a walker returnsto its starting place at the origin after 2n steps isgiven by p2n = = ( ). Hint: Think of choosing n balls from abox that has 2n balls, n white and n black. (c) Conclude that p2n ~ 1/pi n as n - > infinity. (d) Conclude that the two - dimensional walk is recurrent. (b) Show that

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