Asymptotic behavior of the transition probability of a random walk on an infinite graph
Ideas cultivated in spectral geometry are applied to obtain an asymptotic property of a
reversible random walk on an infinite graph satisfying a certain periodic condition. In the
course of our argument, we employ perturbation theory for the maximal eigenvalues of
twisted transition operator. As a result, an asymptotic of the probabilityp (n, x, y) that a
particle starting atxreachesyat timenasngoes to infinity is established.
reversible random walk on an infinite graph satisfying a certain periodic condition. In the
course of our argument, we employ perturbation theory for the maximal eigenvalues of
twisted transition operator. As a result, an asymptotic of the probabilityp (n, x, y) that a
particle starting atxreachesyat timenasngoes to infinity is established.
Ideas cultivated in spectral geometry are applied to obtain an asymptotic property of a reversible random walk on an infinite graph satisfying a certain periodic condition. In the course of our argument, we employ perturbation theory for the maximal eigenvalues of twisted transition operator. As a result, an asymptotic of the probabilityp(n,x,y) that a particle starting atxreachesyat timenasngoes to infinity is established.
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