English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study a stochastic particle system which is motivated from grain boundarycoarsening in two-dimensional networks. Each particles lives on the positivereal line and is labeled as belonging to either Species 1 or Species 2. Species1 particles drift at unit speed toward the origin, while Species 2 particles donot move. When a particle in Species 1 hits the origin, it is removed, and arandomly selected particle mutates from Species 2 to Species 1. The processdescribed is an example of a high-dimensional piecewise deterministic Markovprocess (PDMP), in which deterministic flow is punctuated with stochasticjumps. Our main result is a proof of exponential concentration inequalities ofthe Kolmogorov-Smirnoff distance between empirical measures of the particlesystem and solutions of limiting nonlinear kinetic equations. Our method ofproof involves a time and space discretization of the kinetic equations, whichwe compare with the particle system to derive recurrence inequalities forcomparing total numbers in small intervals. To show these recurrences occurwith high probability, we appeal to a state dependent Hoeffding type inequalityat each time increment.

Concentration inequalities for the hydrodynamic limit of a two-species stochastic particle system