S. Nakajima

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20242026

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7 papers · 1 filter

math.PR2026

A quantitative replica-symmetric bound of Sherrington--Kirkpatrick model in the entire de Almeida--Thouless region

Seiichiro Kusuoka, Shuta Nakajima

We consider the Sherrington--Kirkpatrick model with inverse temperature $β > 0$ and deterministic external field $h > 0$ . Let $q$ be the replica-symmetric fixed point: $q=\mathbb E{\rm…

math.PR2026

A note on Lata\la's argument in SK model

Seiichiro Kusuoka, Shuta Nakajima

In this note, we consider the Sherrington--Kirkpatrick model with deterministic external field. Let $q = q (I^^{2}, h)$ denote the solution of the replica-symmetric self-consistency equati…

math.PR2025

Uniqueness of Replica-symmetric Saddle Point for Ising Perceptron

Shuta Nakajima

We study the replica-symmetric saddle point equations for the Ising perceptron with Gaussian disorder and margin $I^º \geq 0$ . We prove that for each $I^º \geq 0$ there is a critical cap…

math.PR2025

Moderate deviations in first-passage percolation for bounded weights

Wai-Kit Lam, Shuta Nakajima

We investigate the moderate and large deviations in first-passage percolation (FPP) with bounded weights on $Z^{d}$ for $d \geq 2$ . Write $T (x, y)$ for the…

math.PR2025

Equivalence of fluctuations of discretized SHE and KPZ equations in the subcritical weak disorder regime

Stefan Junk, Shuta Nakajima

We study the fluctuations of discretized versions of the stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation in spatial dimensions $d \geq 3$ in the weak disor…

math.PR2025

The maximum of the two dimensional Gaussian directed polymer in the subcritical regime

We study the maximum $I ¨ _{N}^{*}$ of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an $N \times N$ box. We show that $Ï_N^*/\l…