A Random Walk with Exponential Travel Times

الموضوعات : مجله بین المللی ریاضیات صنعتی

R. Kazemi ¹ (Department of Statistics, Imam Khomeini International University, Qazvin, Iran)

تاريخ الإرسال : 11 الخميس , محرم, 1435 تاريخ التأكيد : 11 الخميس , محرم, 1435 تاريخ الإصدار : 09 الإثنين , صفر, 1436

الکلمات المفتاحية: Smallest path, Random Walk, Pure birth process, Random recursive trees,

ملخص المقالة :

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.