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- W4300880080 abstract "We prove exponential concentration estimates and a strong law of large numbers for a particle system that is the simplest representative of a general class of models for 2D grain boundary coarsening. The system consists of $n$ particles in $(0,infty)$ that move at unit speed to the left. Each time a particle hits the boundary point $0$, it is removed from the system along with a second particle chosen uniformly from the particles in $(0,infty)$. Under the assumption that the initial empirical measure of the particle system converges weakly to a measure with density $f_0(x) in L^1_+(0,infty)$, the empirical measure of the particle system at time $t$ is shown to converge to the measure with density $f(x,t)$, where $f$ is the unique solution to the kinetic equation with nonlinear boundary coupling $$partial_t f (x,t) - partial_x f(x,t) = -frac{f(0,t)}{int_0^infty f(y,t), dy} f(x,t), quad 0<x < infty, $$ and initial condition $f(x,0)=f_0(x)$. The proof relies on a concentration inequality for an urn model studied by Pittel, and Maurey's concentration inequality for Lipschitz functions on the permutation group." @default.
- W4300880080 created "2022-10-04" @default.
- W4300880080 creator A5065480740 @default.
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- W4300880080 date "2016-08-09" @default.
- W4300880080 modified "2023-09-28" @default.
- W4300880080 title "Concentration inequalities for a removal-driven thinning process" @default.
- W4300880080 doi "https://doi.org/10.48550/arxiv.1608.02822" @default.
- W4300880080 hasPublicationYear "2016" @default.
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