Random Walk on a Connected Graph |
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assumption chooses uniformly CONNECTED GRAPH CORNELL UNIVERSITY LIBRARY 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 ɛ î let February Feller given graduate Hence i,j ɛ i.e. Lim In(t increase of F independent India initial integer integral multiples irreducible join June length Lim n(t Lim t+ limiting behaviour Markov chain measurable function Model Let motion n+1 n+1 Nij n(t Nij w number of visits o-algebra obtain particle path Po[w Po[w:X₂ points of increase Polw probability Proof Punjab random variable RANDOM WALK Renewal Research Shashi Prabha Phoha SPECIALIZATION speed Spitzer stochastic summing T¹³ Teaching Assistantship tends to infinity thanks Thesis Tijk transition matrix uniform unique UNIV vertex ε Ω ω εΩ