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Question: ely often with probabili ity 11 consider a twodimensional random...

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ely often with probabili ity 11 Consider a two-dimensional random walk in which a particle moves between the int n ns of the ollowin {(hj) : i, j = that 0< pq,rs1 time n + 1 is points li corr 10,1,·.) with integer coordinatesinthe plane. Iet p,q, r, s be numbers such r. 1 and p+qtr+s, If the particlc is at position (i. j) at time n, its position at and (i + 1, j) with probability p. j+ 1) with probability q. 1, j) with probability r. (i.j 1) with probability s. walk essive moves are independent of each other. Writing Sn for the position of the particle after moves, we have that Sn (1,0) with probability p. Sn (0, 1) with probability q Sn (1,0) with probability r, S (0,1) with probability s, Sn+1 = (0, 0). Let vn P(S (0, 0)) be the probability that the particle revisits is and we suppose that So starting point at time n. Show that vn 0 if n is odd and he walk ible if n . From m (2m) k!2 (m - k)!2 k-0

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