Related papers: The conditional Gaussian multiplicative chaos stru…
We consider Gaussian multiplicative chaos measures defined in a general setting of metric measure spaces. Uniqueness results are obtained, verifying that different sequences of approximating Gaussian fields lead to the same chaos measure.…
We prove a distributional limit theorem conjectured in [Journal of Statistical Physics 174, No. 6, 1372-1403 (2019)] for partition functions defining models of directed polymers on diamond hierarchical graphs with disorder variables placed…
We consider a sub-critical Gaussian multiplicative chaos (GMC) measure defined on the unit interval [0,1] and prove an exact formula for the fractional moments of the total mass of this measure. Our formula includes the case where…
We present a simple criterion, only based on second moment assumptions, for the convergence of polynomial or Wiener chaos to a Gaussian limit. We exploit this criterion to obtain new Gaussian asymptotics for the partition functions of…
We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measures converge stably to a nontrivial limit. This limit depends…
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.…
This review-style article presents an overview of recent progress in constructing and studying critical Gaussian multiplicative chaos. A proof that the critical measure in any dimension can be obtained as a limit of subcritical measures is…
As represented by the Liouville measure, Gaussian multiplicative chaos is a random measure constructed from a Gaussian field. Under certain technical assumptions, we prove the convergence of a process time-changed by Gaussian multiplicative…
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…
Let $M_{\gamma}$ be a subcritical Gaussian multiplicative chaos measure associated with a general log-correlated Gaussian field defined on a bounded domain $D \subset \mathbb{R}^d$, $d \geq 1$. We find an explicit formula for its…
We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications.…
In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in…
Let $\alpha$ be a Steinhaus random multiplicative function. For a wide class of multiplicative functions $f$ we construct a multiplicative chaos measure arising from the Dirichlet series of $\alpha f$, in the whole $L^1$-regime. Our method…
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…
A variational method that allows for replica-symmetry breaking is applied to directed polymers in an (N+1)-dimensional disordered medium. The noise studied here has gaussian correlations, i.e. it is short-ranged. In dimensions N<2, the…
We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we…
We derive a semi-analytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor-axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of…
A completely elementary and self-contained proof of convergence of Gaussian multiplicative chaos is given. The argument shows further that the limiting random measure is nontrivial in the entire subcritical phase $(\gamma < \sqrt{2d})$ and…
In the spirit of [M. Biskup & O. Louidor, Adv. Math. 330 (2018)], we study the local structure of $\star$-scale invariant fields -- a class of log-correlated Gaussian fields -- around their extremal points by characterising the law of the…
The holomorphic multiplicative chaos (HMC) is a holomorphic analogue of the Gaussian multiplicative chaos. It arises naturally as the limit in large matrix size of the characteristic polynomial of Haar unitary matrices, and more generally,…