Abstract
In sufficiently low-dimensional systems, the conditional mean time to return to the starting site (conditional upon return eventually occuring) is infinite. We examine the conditional mean time τ n to return in a walk of finite duration n steps. For walks of Pólya type, τ n is found asymptotically proportional to `√ n, n log 2 n , √ n and log n in dimensions 1, 2, 3 and 4 respectively. Results are also given for walks with long-ranged transitions, and for a one-dimensional walk in a central potential.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Physica A: Statistical Mechanics and its Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.