作者：Turner, Amanda G.
作者单位：University of Cambridge
摘要：We consider sequences (X-t(N))t >= 0 of Markov processes in two dimensions whose fluid limit is a stable solution of an ordinary differential equation of the form x(t) = b(x(t)), where b(x) = ((-mu)(0)(0)(lambda))x + tau(x) for some lambda, mu > 0 and tau(x) = 0(vertical bar x vertical bar(2)). Here the processes are indexed so that the variance of the fluctuations of X-t(N) is inversely proportional to N. The simplest example t arises from the OK Corral gunfight model which was formulated by ...
作者：Garet, Olivier; Marchand, Regine
作者单位：Universite de Orleans; Universite de Lorraine
摘要：The chemical distance D(x, y) is the length of the shortest open path between two points x and y in an infinite Bernoulli percolation cluster. In this work, we study the asymptotic behavior of this random metric, and we prove that, for an appropriate norm mu depending on the dimension and the percolation parameter, the probability of the event {0 <-> x, D(0, x)/mu(x) is not an element of (1 - epsilon, 1 + epsilon} exponentially decreases when vertical bar vertical bar x vertical bar vertical b...
作者：Watanabe, Toshiro
作者单位：University of Aizu
摘要：A necessary and sufficient condition for the almost sure existence of an absolutely continuous (with respect to the branching measure) exact Hausdorff measure on the boundary of a Galton-Watson tree is obtained. In the case where the absolutely continuous exact Hausdorff measure does not exist almost surely, a criterion which classifies gauge functions phi according to whether pi-Hausdorff measure of the boundary minus a certain exceptional set is zero or infinity is given. Important examples ...
