Yi Han

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20232026

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math.PR2026

Brown measure convergence for the spectrum of polynomials in Ginibre matrices

Yi Han

Fix a multivariate polynomial $p$ in $n$ non-commuting variables of arbitrary degree, and consider $n$ independent $N \times N$ complex Ginibre matrices $X_1^N,\cdots,X_n…

math.PR2026

Glauber dynamics for random field Ising models on bounded degree graphs and MLSI

Yi Han

We study the ferromagnetic random field Ising model (RFIM) on a graph $G = (V, E)$ having maximal degree $Δ$ , where the external field at each vertex is an i.i.d. random variable. Whe…

math.PR2024

Deformed Fréchet law for Wigner and sample covariance matrices with tail in crossover regime

Yi Han

Given $A_{n} := \frac{1}{n} (a_{ij})$ an $n \times n$ symmetric random matrix, with elements above the diagonal given by i.i.d. random variables having mean zero and unit variance…

math.PR2023

Deviation of top eigenvalue for some tridiagonal matrices under various moment assumptions

Yi Han

Symmetric tridiagonal matrices appear ubiquitously in mathematical physics, serving as the matrix representation of discrete random Schrödinger operators. In this work we investiga…

math.PR2023

Symmetric matrices with banded heavy tail noise: local law and eigenvector delocalization

Yi Han

In this work we consider deterministic, symmetric matrices with heavy-tailed noise imposed on entries within a fixed distance $K$ to the diagonal. The most important example is dis…