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- W3103189986 abstract "We have considered the persistence of unvisited sites of a lattice, i.e., the probability $S(t)$ that a site remains unvisited till time $t$ in presence of mutually repulsive random walkers. The dynamics of this system has direct correspondence to that of the domain walls in a certain system of Ising spins where the number of domain walls become fixed following a zero termperature quench. Here we get the result that $S(t) propto exp(-alpha t^{beta})$ where $beta$ is close to 0.5 and $alpha$ a function of the density of the walkers $rho$. The number of persistent sites in presence of independent walkers of density $rho^prime$ is known to be $S^prime (t) = exp(-2 sqrt{frac{2}{pi}} rho^prime t^{1/2})$. We show that a mapping of the interacting walkers' problem to the independent walkers' problem is possible with $rho^prime = rho/(1-rho)$ provided $rho^prime, rho$ are small. We also discuss some other intricate results obtained in the interacting walkers' case." @default.
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- W3103189986 date "2007-05-22" @default.
- W3103189986 modified "2023-09-27" @default.
- W3103189986 title "Dynamics of unvisited sites in the presence of mutually repulsive random walkers" @default.
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- W3103189986 doi "https://doi.org/10.1088/1751-8113/40/23/001" @default.
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