A Random Walk with Exponential Travel Times

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

R. Kazemi ¹

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

تاریخ دریافت : 1392/08/23 تاریخ پذیرش : 1392/08/23 تاریخ انتشار : 1393/09/10

کلید واژه: Smallest path, Random Walk, Pure birth process, Random recursive trees,

چکیده مقاله :

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