Density and correlation in a random sequential adsorption model

2022/10/11 by Charles S. Amaral, Amaral, Charles S. do, Diogo C. dos Santos +1
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Random Matrices and Applications #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2210.05627

Abstract

We consider a random sequential adsorption process on the one-dimensional lattice with nearest-neighbor exclusion. In this model, each site s ∈ ℤ starts empty and we will try to occupy it in time t_s, where (t_s)_s∈ℤ is a sequence of independent random variables uniformly distributed on the interval [0,1]. The site will be occupied if both of its neighbors are vacant. We provide a method to calculate the density of occupied sites up to the time t, as well as the pair correlation function.

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