Occupancy of a single site by many random walkers
We consider an infinite number of noninteracting lattice random walkers with the goal of determining statistical properties of the time, out of a total time T, that a single site has been occupied by n random walkers. Initially the random walkers are assumed uniformly distributed on the lattice exce...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2000 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/18825 |
| Acceso en línea: | https://hdl.handle.net/2445/18825 |
| Access Level: | acceso abierto |
| Palabra clave: | Física estadística Termodinàmica Sistemes no lineals Física matemàtica Statistical physics Thermodynamics Nonlinear systems Mathematical physics |
| Sumario: | We consider an infinite number of noninteracting lattice random walkers with the goal of determining statistical properties of the time, out of a total time T, that a single site has been occupied by n random walkers. Initially the random walkers are assumed uniformly distributed on the lattice except for the target site at the origin, which is unoccupied. The random-walk model is taken to be a continuous-time random walk and the pausing-time density at the target site is allowed to differ from the pausing-time density at other sites. We calculate the dependence of the mean time of occupancy by n random walkers as a function of n and the observation time T. We also find the variance for the cumulative time during which the site is unoccupied. The large-T behavior of the variance differs according as the random walk is transient or recurrent. It is shown that the variance is proportional to T at large T in three or more dimensions, it is proportional to T3/2 in one dimension and to TlnT in two dimensions. |
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