Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.25364

Bulk universality of scaling limits for the almost Hermitian Coulomb gas

Yacin Ameur
View original source ↗Read source document ↗Export metadata ↓

Abstract

Inspired by the recent approach to edge universality of Cronvall and Wennman, we prove several local universality results for scaling limits in the bulk in the almost Hermitian regime, as well as associated results relating to reproducing kernel spaces of the Fock type.

Explore related subjects

math.PR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yacin Ameur. 2026-10-18. Bulk universality of scaling limits for the almost Hermitian Coulomb gas. https://arxiv.org/abs/2610.25364

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Well-posedness of kinetic McKean-Vlasov equations

We consider the McKean-Vlasov equation $dX_t = b(t, X_t, [X_t])dt + σ(t, X_t, [X_t])dW_t$ where $[X_t]$ is the law of $X_t$. We specifically consider the kinetic case, where the equation is degenerate because the dimension of the Brownian motion $W$ is strictly smaller than that of the solution $X$, as commonly required in classical models of collisional kinetic theory. Assuming Hölder continuous coefficients and a weak Hörmander condition, we prove the well-posedness of the equation. This result advances the existing literature by filling a crucial gap: it addresses the previously unexplored case where the diffusion coefficient $σ$ depends on the law $[X_t]$. Notably, our proof employs a simplified and direct argument eliminating the need for PDEs involving derivatives with respect to the measure argument. A critical ingredient is the sub-Riemannian metric structure induced by the corresponding Fokker-Planck operator.

math.PR↗
arXiv2026

Ergodic properties of the harmonic process

In this paper we study detailed fluctuation results for a class of non-equilibrium steady states. The main example is the boundary driven harmonic model \cite{frassek2022exact}. In this model, the non-equilibrium steady state (NESS) is a mixture of products of geometric distributions, of which the local parameters are in turn distributed as uniform order statistics. For such a NESS, we prove law of large numbers, central limit theorem and large deviation results for fields of a general local functions (generalizing the density field). We also obtain quantitative results on the deviation from local equilibrium.

math.PR↗
arXiv2026

First pair coalescence among three geodesics

In directed last-passage percolation with i.i.d. exponential vertex weights, the coalescence time $\operatorname{Coal}(a,b)$ of two semi-infinite geodesics started from vertices $a$ and $b$ in a fixed direction has a heavy tail with (KPZ) exponent $2/3$, and hence infinite expectation. We study instead the first coalescence among triples of semi-infinite geodesics in first- and last-passage percolation models (FPP/LPP) on $\mathbb{Z}^2$ that arise from stationary compatible families, such as Busemann geodesics. For directed FPP and LPP with arbitrary weights, we prove that $$\mathbb{E}\bigl[\min\{\operatorname{Coal}(a,a-e_1),\operatorname{Coal}(a,a-e_2)\}\bigr]<\infty.$$ We also consider FPP and LPP models in which antidiagonal motion is allowed, and prove that for every integer $k>0$, \[\mathbb{E}\bigl[\min\{\operatorname{Coal}(a,a-k(e_1-e_2)),\operatorname{Coal}(a,a+k(e_1-e_2))\}\bigr]<\infty.\] These results support the heuristic prediction that adjacent coalescence times are negatively associated.

math.PR↗