Pith. sign in

REVIEW 1 cited by

Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2011.01751 v1 pith:W7EF6RYZ submitted 2020-11-03 math.PR math.CO

Jiaoyang Huang This is my paper · ORCID
classification math.PRmath.CO
keywords randomheightfluctuationslozengenonintersectingtilingswalksbernoulli
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

In this paper we study height fluctuations of random lozenge tilings of polygonal domains on the triangular lattice through nonintersecting Bernoulli random walks. For a large class of polygons which have exactly one horizontal upper boundary edge, we show that these random height functions converge to a Gaussian Free Field as predicted by Kenyon and Okounkov [28]. A key ingredient of our proof is a dynamical version of the discrete loop equations as introduced by Borodin, Guionnet and Gorin [5], which might be of independent interest.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models

    math.PR 2025-02 conditional novelty 7.0 of 10

    Periodic Aztec diamond height fluctuations are shown to decompose into a Gaussian free field plus a discrete-Gaussian random harmonic component.

Pith tools