Split-and-Merge in Stationary Random Stirring on Lattice Torus

Dmitri Ioffe; Balint A Toth

doi:10.1007/s10955-020-02487-2

Split-and-Merge in Stationary Random Stirring on Lattice Torus

Dmitri Ioffe, Balint A Toth^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

64 Downloads (Pure)

Abstract

We show that in any dimension d≥1, the cycle-length process of stationary random stirring (or, random interchange) on the lattice torus converges to the canonical Markovian split-and-merge process with the invariant (and reversible) measure given by the Poisson–Dirichlet law PD(1), as the size of the system grows to infinity. In the case of transient dimensions, d≥3, the problem is motivated by attempts to understand the onset of long range order in quantum Heisenberg models via random loop representations of the latter.

Original language	English
Pages (from-to)	630–653
Number of pages	24
Journal	Journal of Statistical Physics
Volume	180
DOIs	https://doi.org/10.1007/s10955-020-02487-2
Publication status	Published - 1 Feb 2020

Keywords

random interchange process
split-and-merge
Poisson-Dirichlet distribution
quantum Heisenberg model

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Professor Balint A Toth
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- School of Mathematics - Chair in Probability
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title = "Split-and-Merge in Stationary Random Stirring on Lattice Torus",

abstract = "We show that in any dimension d≥1, the cycle-length process of stationary random stirring (or, random interchange) on the lattice torus converges to the canonical Markovian split-and-merge process with the invariant (and reversible) measure given by the Poisson–Dirichlet law PD(1), as the size of the system grows to infinity. In the case of transient dimensions, d≥3, the problem is motivated by attempts to understand the onset of long range order in quantum Heisenberg models via random loop representations of the latter.",

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doi = "10.1007/s10955-020-02487-2",

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T1 - Split-and-Merge in Stationary Random Stirring on Lattice Torus

AU - Ioffe, Dmitri

AU - Toth, Balint A

PY - 2020/2/1

Y1 - 2020/2/1

N2 - We show that in any dimension d≥1, the cycle-length process of stationary random stirring (or, random interchange) on the lattice torus converges to the canonical Markovian split-and-merge process with the invariant (and reversible) measure given by the Poisson–Dirichlet law PD(1), as the size of the system grows to infinity. In the case of transient dimensions, d≥3, the problem is motivated by attempts to understand the onset of long range order in quantum Heisenberg models via random loop representations of the latter.

AB - We show that in any dimension d≥1, the cycle-length process of stationary random stirring (or, random interchange) on the lattice torus converges to the canonical Markovian split-and-merge process with the invariant (and reversible) measure given by the Poisson–Dirichlet law PD(1), as the size of the system grows to infinity. In the case of transient dimensions, d≥3, the problem is motivated by attempts to understand the onset of long range order in quantum Heisenberg models via random loop representations of the latter.

KW - random interchange process

KW - split-and-merge

KW - Poisson-Dirichlet distribution

KW - quantum Heisenberg model

U2 - 10.1007/s10955-020-02487-2

DO - 10.1007/s10955-020-02487-2

M3 - Article (Academic Journal)

SN - 0022-4715

VL - 180

SP - 630

EP - 653

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

ER -

Split-and-Merge in Stationary Random Stirring on Lattice Torus

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