László Erdős

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20242026

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5 papers · 1 filter

math.PR2024

Density of Brown measure of free circular Brownian motion

LÃ¡szlÃ³ ErdÅs, Hong Chang Ji

We consider the Brown measure of the free circular Brownian motion, $a + t x$ , with an arbitrary initial condition $a$ , i.e. $\boldsymbol…

math.PR2024

Cusp Universality for Correlated Random Matrices

LÃ¡szlÃ³ ErdÅs, Joscha Henheik, Volodymyr Riabov

For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states…

math-ph2024

Loschmidt Echo for Deformed Wigner Matrices

LÃ¡szlÃ³ ErdÅs, Joscha Henheik, Oleksii Kolupaiev

We consider two Hamiltonians that are close to each other, $H_{1} \approx H_{2}$ , and analyze the time-decay of the corresponding Loschmidt echo $\mathfrak{M}(t) := |\langle Ï_0, \ma…

math.PR2024

Eigenstate Thermalization Hypothesis for Wigner-type Matrices

Volodymyr Riabov, LÃ¡szlÃ³ ErdÅs

We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for observa…

math.PR2024

Mesoscopic Central Limit Theorem for non-Hermitian Random Matrices

Giorgio Cipolloni, LÃ¡szlÃ³ EndÅs, Dominik SchrÃ¶der

We prove that the mesoscopic linear statistics $\sum_{i} f (n^{a} (I ¨ _{i} - z_{0}))$ of the eigenvalues ${I ¨ _{i}}_{i}$ of large $n \times n$ non-Hermitian random matrices with complex centred i.i…