Related papers: Critical Gaussian Multiplicative Chaos for singula…
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 the distribution of the total mass of the measure, and an…
We consider $N\times N$ matrices $X$ with independent, identically distributed entries, and prove that the sequence of measures $\frac{ | \det (X-z)|^\gamma}{\mathbb{E}[ | \det (X-z)|^\gamma]}$ converge to the Gaussian Multiplicative Chaos…
In the present paper, we show that (under some minor technical assumption) Complex Gaussian Multiplicative Chaos defined as the complex exponential of a $\log$-correlated Gaussian field can be obtained by taking the limit of the exponential…
We consider log-correlated random fields $X$ and the associated multiplicative chaos measures $\mu_{\gamma,X}$. Our results reconstruct the underlying field $X$ from the multiplicative chaos measure $\nu_{\gamma,X}$. The new feature of our…
For an $N \times N$ random unitary matrix $U_N$, we consider the random field defined by counting the number of eigenvalues of $U_N$ in a mesoscopic arc of the unit circle, regularized at an $N$-dependent scale $\epsilon_N>0$. We prove that…
The aim of this review-style paper is to provide a concise, self-contained and unified presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) measures for log-correlated fields in 2D in the subcritical…
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 covers the whole subcritical phase and only requires…
Denote by $\mu_\beta="\exp(\beta X)"$ the Gaussian multiplicative chaos which is defined using a log-correlated Gaussian field $X$ on a domain $U\subset\mathbb{R}^d$. The case $\beta\in\mathbb{R}$ has been studied quite intensively, and…
We consider powers of the absolute value of the characteristic polynomial of Haar distributed random orthogonal or symplectic matrices, as well as powers of the exponential of its argument, as a random measure on the unit circle minus small…
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 of the matrix tends to infinity, to a Gaussian…
In this article, we consider the multiplicative chaos measure associated to the log-correlated random Fourier series, or random wave model, with i.i.d. coefficients taken from a general class of distributions. This measure was shown to be…
Given an instance $h$ of the Gaussian free field on a planar domain $D$ and a constant $\gamma \in (0,2)$, one can use various regularization procedures to make sense of the Liouville quantum gravity area measure $\mu := e^{\gamma h(z)}…
In this paper, we establish the exact Fourier dimensions of all standard sub-critical Gaussian multiplicative chaos on the unit interval, thereby confirming the Garban-Vargas conjecture. The proof relies on a significant improvement of the…
In this article we study imaginary Gaussian multiplicative chaos -- namely a family of random generalized functions which can formally be written as $e^{i X(x)}$, where $X$ is a log-correlated real-valued Gaussian field on $\mathbb{R}^d$,…
We identify an equality between two objects arising from different contexts of mathematical physics: Kahane's Gaussian Multiplicative Chaos ($GMC^\gamma$) on the circle, and the Circular Beta Ensemble $(C\beta E)$ from Random Matrix Theory.…
We characterise the multiplicative chaos measure $\mathcal{M}$ associated to planar Brownian motion introduced in [BBK94,AHS20,Jeg20a] by showing that it is the only random Borel measure satisfying a list of natural properties. These…
We study the total mass of high points in a random model for the Riemann-Zeta function. We consider the same model as in [8], [2], and build on the convergence to 'Gaussian' multiplicative chaos proved in [14]. We show that the total mass…
We introduce a unified approach for studying the polynomial Fourier decay of classical multiplicative chaos measures. As consequences, we obtain the precise Fourier dimensions for multiplicative chaos measures arising from the following key…
The objective of this note is to study the probability that the total mass of a sub-critical Gaussian multiplicative chaos (GMC) with arbitrary base measure $\sigma$ is small. When $\sigma$ has some continuous density w.r.t Lebesgue…
Consider a logarithmically-correlated Gaussian field $X$ in $d$ dimensions. For all $\gamma \in (-\sqrt{2d},\sqrt{2d})$, we show that the derivatives $\frac{\partial^k}{\partial\gamma^k} :e^{\gamma X_\epsilon}:$ of the regularised Gaussian…