Comparison of partition functions in a space–time random environment

Stefan Junk

doi:10.1007/s10955-020-02566-4

Comparison of partition functions in a space–time random environment

Stefan Junk

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

1 Citation (Scopus)

Abstract

Let Z¹ and Z² be partition functions in the random polymer model in the same environment but driven by different underlying random walks. We give a comparison in concave stochastic order between Z¹ and Z² if one of the random walks has “more randomness” than the other. We also treat some related models: The parabolic Anderson model with space–time Lévy noise; Brownian motion among space–time obstacles; and branching random walks in space–time random environments. We also obtain a necessary and sufficient criterion for Z¹⪯ _cvZ² if the lattice is replaced by a regular tree.

Original language	English
Pages (from-to)	95-115
Number of pages	21
Journal	Journal of Statistical Physics
Volume	181
Issue number	1
DOIs	https://doi.org/10.1007/s10955-020-02566-4
Publication status	Published - 2020 Oct 1
Externally published	Yes

Keywords

Directed polymers
Random environment
Stochastic order

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-020-02566-4

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title = "Comparison of partition functions in a space–time random environment",

abstract = "Let Z1 and Z2 be partition functions in the random polymer model in the same environment but driven by different underlying random walks. We give a comparison in concave stochastic order between Z1 and Z2 if one of the random walks has “more randomness” than the other. We also treat some related models: The parabolic Anderson model with space–time L{\'e}vy noise; Brownian motion among space–time obstacles; and branching random walks in space–time random environments. We also obtain a necessary and sufficient criterion for Z1⪯ cvZ2 if the lattice is replaced by a regular tree.",

keywords = "Directed polymers, Random environment, Stochastic order",

author = "Stefan Junk",

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N2 - Let Z1 and Z2 be partition functions in the random polymer model in the same environment but driven by different underlying random walks. We give a comparison in concave stochastic order between Z1 and Z2 if one of the random walks has “more randomness” than the other. We also treat some related models: The parabolic Anderson model with space–time Lévy noise; Brownian motion among space–time obstacles; and branching random walks in space–time random environments. We also obtain a necessary and sufficient criterion for Z1⪯ cvZ2 if the lattice is replaced by a regular tree.

AB - Let Z1 and Z2 be partition functions in the random polymer model in the same environment but driven by different underlying random walks. We give a comparison in concave stochastic order between Z1 and Z2 if one of the random walks has “more randomness” than the other. We also treat some related models: The parabolic Anderson model with space–time Lévy noise; Brownian motion among space–time obstacles; and branching random walks in space–time random environments. We also obtain a necessary and sufficient criterion for Z1⪯ cvZ2 if the lattice is replaced by a regular tree.

KW - Directed polymers

KW - Random environment

KW - Stochastic order

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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ER -

Comparison of partition functions in a space–time random environment

Abstract

Keywords

ASJC Scopus subject areas

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