## Random walk on a connected graph |

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Assume assumption chooses uniformly CONNECTED GRAPH Consider Cornell University cylinder set events define Degree denotes the expected denotes the number Department of Mathematics directed edge emanating distributed doubly entrance Ergodic Theorem Example exists expected recurrence express extended February Feller fixed given graduate helped Hence i,j e i.e. Lim increase of F independent India initial integral multiples irreducible J J ij join June length limiting behaviour Markov chain measurable function Model Let motion moves number of renewals number of visits obtain otherwise particle PARTICULAR path period Phoha points of increase Presented probability Proof Punjab random variable RANDOM WALK Research Shashi Prabha space SPECIALIZATION speed Spitzer stochastic Study successive summing Teaching tends to infinity thanks Thesis Tn(w Tn+1 transition matrix uniform unique UNIVERSITY LIBRARY vertex w e ft weft let Xt(w