Coarsening with a frozen vertex

Michael Damron; Hana Kogan; Charles M. Newman; Vladas Sidoravicius

doi:10.1214/16-ECP4785

Coarsening with a frozen vertex

Michael Damron, Hana Kogan, Charles M. Newman, Vladas Sidoravicius

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In the standard nearest-neighbor coarsening model with state space {-1,+1} Z² and initial state chosen from symmetric product measure, it is known (see 2.) that almost surely, every vertex flips infinitely often. In this paper, we study the modified model in which a single vertex is frozen to +1 for all time, and show that every other site still flips infinitely often. The proof combines stochastic domination (attractivity) and influence propagation arguments.

Original language	English (US)
Article number	9
Journal	Electronic Communications in Probability
Volume	21
DOIs	https://doi.org/10.1214/16-ECP4785
State	Published - 2016

Keywords

Coarsening models
Frozen vertex
Zero-temperature glauber dynamics

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/16-ECP4785

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abstract = "In the standard nearest-neighbor coarsening model with state space {-1,+1} Z2 and initial state chosen from symmetric product measure, it is known (see 2.) that almost surely, every vertex flips infinitely often. In this paper, we study the modified model in which a single vertex is frozen to +1 for all time, and show that every other site still flips infinitely often. The proof combines stochastic domination (attractivity) and influence propagation arguments.",

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AU - Damron, Michael

AU - Kogan, Hana

AU - Newman, Charles M.

AU - Sidoravicius, Vladas

PY - 2016

Y1 - 2016

N2 - In the standard nearest-neighbor coarsening model with state space {-1,+1} Z2 and initial state chosen from symmetric product measure, it is known (see 2.) that almost surely, every vertex flips infinitely often. In this paper, we study the modified model in which a single vertex is frozen to +1 for all time, and show that every other site still flips infinitely often. The proof combines stochastic domination (attractivity) and influence propagation arguments.

AB - In the standard nearest-neighbor coarsening model with state space {-1,+1} Z2 and initial state chosen from symmetric product measure, it is known (see 2.) that almost surely, every vertex flips infinitely often. In this paper, we study the modified model in which a single vertex is frozen to +1 for all time, and show that every other site still flips infinitely often. The proof combines stochastic domination (attractivity) and influence propagation arguments.

KW - Coarsening models

KW - Frozen vertex

KW - Zero-temperature glauber dynamics

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Coarsening with a frozen vertex

Abstract

Keywords

ASJC Scopus subject areas

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