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Coalescing and branching simple symmetric exclusion process | | Ivailo Hartarsky
; Fabio Martinelli
; Cristina Toninelli
; | | Date: |
2 Jun 2020 | | Abstract: | Motivated by kinetically constrained interacting particle systems (KCM), we
consider a reversible coalescing and branching simple exclusion process on a
general finite graph $G=(V,E)$ dual to the biased voter model on $G$. Our main
goal are tight bounds on its logarithmic Sobolev constant and relaxation time,
with particular focus on the delicate slightly supercritical regime in which
the equilibrium density of particles tends to zero as $|V|
ightarrow infty$.
Our results allow us to recover very directly and improve to $ell^p$-mixing,
$pge 2$, and to more general graphs, the mixing time results of Pillai and
Smith for the FA-$1$f (or $1$-neighbour) KCM on the discrete $d$-dimensional
torus. In view of applications to the more complex FA-$j$f KCM, $j>1$, we also
extend part of the analysis to an analogous process with a more general product
state space. | | Source: | arXiv, 2006.1426 | | Services: | Forum | Review | PDF | Favorites | |
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