Romain Allez

activity

20122015

β

-ensembles and the Gauss-Wigner crossover

88 citations · 166 across the 4 of their papers we have counts for

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3 papers · 1 filter

math.PR2015★ 14 cited

The eigenvectors of Gaussian matrices with an external source

Romain Allez, Joël Bun, Jean-Philippe Bouchaud

We consider a diffusive matrix process $(X_{t})_{t \geq 0}$ defined as $X_{t} := A + H_{t}$ where $A$ is a given deterministic Hermitian matrix and $(H_{t})_{t \geq 0}$ is a Hermitian Brownian mot…

math.PR2014★ 23 cited

From Sine kernel to Poisson statistics

Romain Allez, Laure Dumaz

We study the Sine $_{β}$ process introduced in [B. Valkó and B. Virág. Invent. math. (2009)] when the inverse temperature $β$ tends to 0. This point process has been shown to be the s…

math.PR2012★ 88 cited

Invariant $β$ -ensembles and the Gauss-Wigner crossover

Romain Allez, Jean-Philippe Bouchaud, Alice Guionnet

We define a new diffusive matrix model converging towards the $β$ -Dyson Brownian motion for all $β \in [0, 2]$ that provides an explicit construction of $β$ -ensembles of random matr…

The eigenvectors of Gaussian matrices with an external source

From Sine kernel to Poisson statistics

Invariant β-ensembles and the Gauss-Wigner crossover

Invariant $β$ -ensembles and the Gauss-Wigner crossover