39 citations · 162 across the 18 of their papers we have counts for
20 papers
Multiplicative chaos measures from thick points of log-correlated fields
Janne Junnila, Gaultier Lambert, Christian Webb
We prove that multiplicative chaos measures can be constructed from extreme level sets or thick points of the underlying logarithmically correlated field. We develop a method which…
The Coleman correspondence at the free fermion point
Roland Bauerschmidt, Christian Webb
We prove that the truncated correlation functions of the charge and gradient fields associated with the massless sine-Gordon model on with exist for all coupl…
Discretization of the maximum for the derivatives of a random model of on the critical line
Louis-Pierre Arguin, Frédéric Ouimet, Christian Webb
In this short note, we study the derivatives of all orders for the random field where $…
How much can the eigenvalues of a random Hermitian matrix fluctuate?
Tom Claeys, Benjamin Fahs, Gaultier Lambert +1
The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate o…
Network-based Biased Tree Ensembles (NetBiTE) for Drug Sensitivity Prediction and Drug Sensitivity Biomarker Identification in Cancer
Ali Oskooei, Matteo Manica, Roland Mathis +1
We present the Network-based Biased Tree Ensembles (NetBiTE) method for drug sensitivity prediction and drug sensitivity biomarker identification in cancer using a combination of p…
Multiplicative chaos and the characteristic polynomial of the CUE: the -phase
Miika Nikula, Eero Saksman, Christian Webb
In this note we prove that suitable positive powers of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix converge in law, as the size…
Imaginary multiplicative chaos: Moments, regularity and connections to the Ising model
Janne Junnila, Eero Saksman, Christian Webb
In this article we study imaginary Gaussian multiplicative chaos -- namely a family of random generalized functions which can formally be written as , where is a lo…
Quantitative Normal Approximation of Linear Statistics of -ensembles
Gaultier Lambert, Michel Ledoux, Christian Webb
We present a new approach, inspired by Stein's method, to prove a central limit theorem (CLT) for linear statistics of -ensembles in the one-cut regime. Compared with the previo…
On the moments of the characteristic polynomial of a Ginibre random matrix
Christian Webb, Mo Dick Wong
In this article we study the large asymptotics of complex moments of the absolute value of the characteristic polynomial of a complex Ginibre random matrix with the…
Random Hermitian Matrices and Gaussian Multiplicative Chaos
Nathanaël Berestycki, Christian Webb, Mo Dick Wong
We prove that when suitably normalized, small enough powers of the absolute value of the characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary…
The Riemann zeta function and Gaussian multiplicative chaos: statistics on the critical line
Eero Saksman, Christian Webb
We prove that if is uniformly distributed on , then as , converges to a non-trivial random generalized function, which in turn is id…
Multiplicative chaos measures for a random model of the Riemann zeta function
Eero Saksman, Christian Webb
We prove convergence of a stochastic approximation of powers of the Riemann function to a non-Gaussian multiplicative chaos measure, and prove that this measure is a non-trivia…
Global spectral fluctuations in the Gaussian Unitary Ensemble
Christian Webb
We consider global fluctuations of the spectrum of the GUE. Using results on the linear statistics of such matrices as well as variance bounds on the eigenvalues, we show that unde…
A discrete log gas, discrete Toeplitz determinants with Fisher-Hartwig singularities, and Gaussian Multiplicative Chaos
Christian Webb
We consider a log-gas on a discretization of the unit circle. We prove that if the gas is not too dense, or the number of particles in the gas is not too large compared to the scal…
On the logarithm of the characteristic polynomial of the Ginibre ensemble
Christian Webb
We prove a slightly sharper version of a result of Rider and Virág who proved that after centering, the logarithm of the absolute value of the characteristic polynomial of the Gini…
Linear statistics of the circular -ensemble, Stein's method, and circular Dyson Brownian motion
Christian Webb
We study the linear statistics of the circular -ensemble with a Stein's method argument, where the exchangeable pair is generated through circular Dyson Brownian motion. This ge…
The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The -phase
Christian Webb
We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of…
Basic properties of critical lognormal multiplicative chaos
Julien Barral, Antti Kupiainen, Miika Nikula +2
We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of…
Critical Mandelbrot Cascades
Julien Barral, Antti Kupiainen, Miika Nikula +2
We study Mandelbrot's multiplicative cascade measures at the critical temperature. As has been recently shown by Barral, Rhodes and Vargas (arXiv:1203.5445), an appropriately norma…
Exact asymptotics of the freezing transition of a logarithmically correlated random energy model
Christian Webb
We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic…