Pith. sign in

REVIEW 2 cited by

On the Central Limit Theorem for the log-partition function of 2D directed polymers

Not yet reviewed by Pith; the record is open.

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 2402.14647 v2 pith:UJ22AA5C submitted 2024-02-22 math.PR

classification math.PR
keywords betarandomargumentcentraldirecteddistributionfunctionlimit
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

The log-partition function $ \log W_N(\beta)$ of the two-dimensional directed polymer in random environment is known to converge in distribution to a normal distribution when considering temperature in the subcritical regime $\beta=\beta_N=\hat{\beta}\sqrt{\pi/\log N}$, $\hat{\beta}\in (0,1)$ (Caravenna, Sun, Zygouras, Ann. Appl. Prob. (2017)). In this paper, we present an elementary proof of this result relying on a decoupling argument and the central limit theorem for sums of independent random variables. The argument is inspired by an analogy of the model to branching random walks.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Fractional moments of the Stochastic Heat Flow and 2D Directed Polymers

    math.PR 2026-08 conditional novelty 6.0 of 10

    For 0<p<1, the p-th moment of the critical 2D SHF mass on a small ball is bounded by the second moment raised to a negative power whenever the second moment diverges, uniformly in time, disorder, and radius.

  2. The Critical 2d Stochastic Heat Flow and Related Models

    math.PR 2024-12 conditional novelty 2.0 of 10

    Review of the proof that 2d directed polymer and stochastic heat equation partition functions converge, in a critical window, to a unique object called the critical 2d stochastic heat flow.

Pith tools