In this paper, we develop a new approach to studying the Fourier transform of Gaussian multiplicative chaos. We determine the Fourier dimension of these random measures on tori for every smooth log-correlated covariance and in every dimension, and prove sharp bounds and exact formulas for chaos on natural classes of bounded sets and hypersurfaces in Euclidean space. These results highlight how boundary geometry and multifractal concentration jointly govern Fourier decay, including regimes in which the boundary strictly reduces the Fourier dimension. In the circle setting, this gives a substantially simpler new proof of a conjecture of Garban and Vargas.
We introduce power variations of critical Gaussian multiplicative chaos (GMC) along refining partitions in arbitrary dimension. Under suitable renormalisation, we prove uniform fractional moment bounds via Laplace transform estimates as well as stable convergence to supercritical GMCs. Together, these results provide a...
We study a class of discrete-time interacting particle systems arising from mean-field coupled maps. We establish a Dobrushin-type estimate, a relative entropy estimate and Central Limit Theorem (CLT) type results for this class of systems. First we control the growth of the 1-Wasserstein distance between the empirical...
We prove the existence of an essential spectral gap for convex cocompact complex hyperbolic manifolds under the hypothesis that the limit set does not contain a complex circle. We apply an extension to complex hyperbolic manifolds due to Quan of the approach of Vasy to meromorphic continuation of the resolvent. This al...
We study a broad family of active scalar equations with fractional dissipation on $\mathbb{R}^2$ and prove that their entropy diverges to $-\infty$ at a sharp rate of order $\log t$. The proof is based on a suitable regularization scheme, uniform entropy estimates, and a limiting argument via the Vitali convergence the...
In this article, we announce several new results in the ergodic theory of geodesic flows over uniform visibility manifolds without conjugate points. The topics include the ergodicity with respect to the Liouville measure, uniqueness and Bernoulli properties of the measure of maximal entropy and equilibrium states, coun...
Wei-Sheng Wu· Mathematics Research Reports· 0 citations
Motivated by the recent construction of fractional Gaussian fields on the Sierpinski gasket, we study those Gaussian fields whose covariance function exhibits a logarithmic behavior. We introduce a parametric family of random measures associated with these fields, which can be regarded as the analogue to Liouville quan...
P. A. Ruiz, Eva Kopfer· 0 citations
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