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Publikováno v:
Duke Math. J. 167, no. 12 (2018), 2243-2345
In this paper, we investigate the extremal values of (the logarithm of) the characteristic polynomial of a random unitary matrix whose spectrum is distributed according the Circular Beta Ensemble (C$\beta$E). More precisely, if $X_n$ is this characte
Externí odkaz:
http://arxiv.org/abs/1607.00243
Autor:
Madaule, Thomas
In a seminal paper Biggins and Kyprianou \cite{BKy04} proved the existence of a non degenerate limit for the {\it Derivative martingale} of the branching random walk. As shown in \cite{Aid11} and \cite{Mad11}, this is an object of central importance
Externí odkaz:
http://arxiv.org/abs/1606.03211
Consider a branching random walk on the real line. Madaule showed the renormalized trajectory of an individual selected according to the critical Gibbs measure converges in law to a Brownian meander. Besides, Chen proved that the renormalized traject
Externí odkaz:
http://arxiv.org/abs/1507.04506
Autor:
Kyprianou, Andreas E., Madaule, Thomas
Homogeneous mass fragmentation processes describe the evolution of a unit mass that breaks down randomly into pieces as time. Mathematically speaking, they can be thought of as continuous-time analogues of branching random walks with non-negative dis
Externí odkaz:
http://arxiv.org/abs/1507.01559
We consider the complex branching random walk on a dyadic tree with Gaussian weights on the boundary between the diffuse phase and the glassy phase. We study the branching random walk in the space of continuous functions and establish convergence in
Externí odkaz:
http://arxiv.org/abs/1502.05655
This paper is a complement to the studies on the minimum of a real-valued branching random walk. In the boundary case (Biggins, Kyprianou 2005), A\"{i}d\'ekon in a seminal paper (2013) obtained the convergence in law of the minimum after a suitable r
Externí odkaz:
http://arxiv.org/abs/1406.6971
In this paper, we study complex valued branching Brownian motion in the so-called glassy phase, or also called phase II. In this context, we prove a limit theorem for the complex partition function hence confirming a conjecture formulated by Lacoin a
Externí odkaz:
http://arxiv.org/abs/1310.7775
In this paper, we consider the Gibbs measure associated to a logarithmically correlated random potential (including two dimensional free fields) at low temperature. We prove that the energy landscape freezes and enters in the so-called glassy phase.
Externí odkaz:
http://arxiv.org/abs/1310.5574
Autor:
Madaule, Thomas
We study the maximum of a Gaussian field on $[0,1]^\d$ ($\d \geq 1$) whose correlations decay logarithmically with the distance. Kahane \cite{Kah85} introduced this model to construct mathematically the Gaussian multiplicative chaos in the subcritica
Externí odkaz:
http://arxiv.org/abs/1307.1365