math.PR · 2026-08-17 · No. 87

Probability, 2026-08-17.

1 new papers in math.PR. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

1 entries
  1. 01

    Non-Shattering at and Above the Dynamical Temperature in the Spherical Pure p-Spin Model

    Taegyun Kim

    math.PR · cond-mat.dis-nn · cs.LG · math-ph

    We consider the notion of shattering introduced by Ben Arous and Jagannath for spherical pure $p$-spin glasses with overlap $q$. For every $p\geq 3$ and $0<β\leqβ_{\mathrm{sh}}(p)$, we rule out shattering whenever $q\leq2^{-1/2}$ or $q>\sqrt{(p-2)/(p-1)}$. The proof combines a deterministic $N+1$ bound for disjoint bands in the first range with a general-$p$ sign law showing that their total marked weight has subdominant free energy in the...

    arxiv.org/abs/2608.14369 · PDF

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