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The heat and the landscape I

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arxiv 2008.07241 v1 pith:AYMFIBH6 submitted 2020-08-17 math.PR

Balint Virag This is my paper · ORCID
classification math.PR
keywords convergeconvergencefixedheatlandscapepointpolymerarous-peche
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Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape. In this first part, we show that the O'Connell-Yor polymer and the KPZ equation converge to the KPZ fixed point. The key is that one-dimensional Baik-Ben Arous-Peche statistics characterize the KPZ fixed point. This yields a general and elementary method that shows convergence based on previously established limit theorems. Independently, at the same time and place Quastel and Sharkar gave an unrelated proof of KPZ convergence. The methods invite extensions in different directions: ours to polymer models, and theirs to interacting particle systems.

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Cited by 5 Pith papers

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

  1. Temperature chaos in directed polymers

    math.PR 2026-07 conditional novelty 8.0 of 10

    For beta1 = o(beta2) both tending to infinity, coupled CDRP free energies at beta1 and beta2 converge to two independent directed landscapes; as a byproduct, the directed landscape is a two-dimensional black noise.

  2. Spatial decorrelation of KPZ from narrow wedge

    math.PR 2025-06 accept novelty 8.0 of 10

    For fixed t>0, Cov[h(t,x),h(t,0)] ∼ t/x as x→∞, and the spatial average over [0,N] normalized by sqrt(N log N) converges to sqrt(2) times Brownian motion.

  3. Periodic KPZ fixed point with general initial conditions

    math.PR 2026-03 conditional novelty 7.0 of 10

    For general periodic initial data, the relaxation-time-scale limit of periodic TASEP defines the periodic KPZ fixed point with explicit multipoint distributions.

  4. Two-time spatial decorrelation for the flat KPZ fixed point

    math.PR 2026-07 conditional novelty 6.0 of 10

    The two-time spatial covariance of the flat KPZ fixed point decays as exp(-c|x|^3), and normalized spatial averages converge to a Gaussian process with covariance equal to the space-integrated two-time correlation.

  5. Dynamic scaling of growing interfaces

    cond-mat.dis-nn 2025-07 unverdicted novelty 1.0 of 10

    An expert review of the KPZ equation's history, mathematical developments, and applications, with no new research results.

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