A Random Walk with Exponential Travel Times

Document Type : Research Paper


Department of Statistics, Imam Khomeini International University, Qazvin, Iran


Consider the random walk among N places with N(- 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log N as Np is large.