On the Disconnection of a Discrete Cylinder by a Biased Random Walk
نویسنده
چکیده
We consider a random walk on the discrete cylinder (Z/NZ)×Z, d ≥ 3 with drift N in the Z-direction and investigate the large N -behavior of the disconnection time T disc N , defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent α is strictly greater than 1, the asymptotic behavior of T disc N remains N, as in the unbiased case considered by Dembo and Sznitman, whereas for α < 1, the asymptotic behavior of T disc N becomes exponential in N .
منابع مشابه
On the Disconnection of a Discrete Cylinder by a Biased Random Walk by David Windisch
We consider a random walk on the discrete cylinder (Z/NZ)d×Z, d ≥ 3 with drift N−dα in the Z-direction and investigate the large N -behavior of the disconnection time T disc N , defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent α is strictly greater than 1, the asymptotic behavior ...
متن کاملA Lower Bound on the Disconnection Time of a Discrete Cylinder
We study the asymptotic behavior for large N of the disconnection time TN of simple random walk on the discrete cylinder (Z/NZ)d × Z. When d is sufficiently large, we are able to substantially improve the lower bounds on TN previously derived in [3], for d ≥ 2. We show here that the laws of N/TN are tight.
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملDirect Numerical Simulation of the Wake Flow Behind a Cylinder Using Random Vortex Method in Medium to High Reynolds Numbers
Direct numerical simulation of turbulent flow behind a cylinder, wake flow, using the random vortex method for an incompressible fluid in two dimensions is presented. In the random vortex method, the primary variable is vorticity of the flow field. After generation on the cylinder wall, it is followed in two fractional time step in a Lagrangian system of coordinates, namely convection and diffu...
متن کاملComparison of mean hitting times for a degree-biased random walk
Consider the random walk on graphs such that, at each step, the next visited vertex is a neighbor of the current vertex, chosen with probability proportional to the inverse of the square root of its degree. On one hand, for every graph with n vertices, the maximal mean hitting time for this degree-biased random walk is asymptotically dominated by n. On the other hand, the maximal mean hitting t...
متن کامل