Hao Wu

National University of Singapore | NUS · Department of Mathematics

Let f be a meromorphic correspondence on a compact Kähler manifold X of dimension k. Assume that its topological degree is larger than the dynamical degree of order k-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \set...

Let μ be a probability measure on GLd(R) and denote by Sn:=gn⋯g1 the associated random matrix product, where gj’s are i.i.d.’s with law μ. We study statistical properties of random variables of the form σ(Sn,x)+u(Snx),where x∈Pd-1, σ is the norm cocycle and u belongs to a class of admissible functions on Pd-1 with values in R∪{±∞}. Assuming that μ...

We obtain various new limit theorems for random walks on SL2(C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{SL}_2({\mathbb {C}})$$\end{document} under low mo...

Let $f$ be a meromorphic correspondence on a compact K\"ahler manifold $X$ of dimension $k$. Assume that its topological degree is larger than the dynamical degree of order $k-1$. We obtain a quantitative regularity of the equilibrium measure of $f$ in terms of its super-potentials.

Let $\mu $ be a probability measure on $\mathrm {GL}_d(\mathbb {R})$ , and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law $\mu $ . Under the assumptions that $\mu $ has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we prove a Berry–Esseen bound with t...

Let $\mu$ be a probability measure on $\GL_d(\R)$ and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$'s are i.i.d.'s with law $\mu$. We study statistical properties of random variables of the form $$\sigma(S_n,x) + u(S_n x),$$ where $x \in \P^{d-1}$, $\sigma$ is the norm cocycle and $u$ belongs to a class of admis...

Let $\mu$ be a probability measure on $\text{GL}_d(\mathbb{R})$ and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law $\mu$. Under the assumptions that $\mu$ has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we prove a Berry-Esseen bound with the optimal...

Let f be a Hénon–Sibony map, also known as a regular polynomial automorphism of $\mathbb {C}^k$ , and let $\mu $ be the equilibrium measure of f . In this paper we prove that $\mu $ is exponentially mixing for plurisubharmonic observables.

Let $\nu$ be the Furstenberg measure associated with a non-elementary probability measure $\mu$ on SL_2(R). We show that, when $\mu$ has a finite second moment, the Fourier coefficients of $\nu$ tend to zero at infinity. In other words, $\nu$ is a Rajchman measure. This improves a recent result of Jialun Li.

We obtain new limit theorems for random walks on SL_2(C) under low moment conditions. For non-elementary measures with a finite second moment we prove a Local Limit Theorem for the norm cocycle, yielding the optimal version of a theorem of E. Le Page. For measures with a finite third moment we obtain a Local Limit Theorem for the matrix coefficient...

We study local positive d d c dd^{c} -closed currents directed by a foliation by Riemann surfaces near a hyperbolic singularity which have no mass on the separatrices. A theorem of Nguyên says that the Lelong number of such a current at the singular point vanishes. We prove that this property is sharp: one cannot have any better mass estimate for t...

We study local positive harmonic currents directed by a foliation by Riemann surfaces near a hyperbolic singularity which have no mass on the separatrices. A theorem of Nguy\^en says that the Lelong number of such a current at the singular point vanishes. We prove that this property is sharp: one cannot have any better mass estimate for this curren...

Let $f$ be a holomorphic automorphism of positive entropy on a compact K\"ahler manifold. Assume moreover that $f$ admits a unique maximal dynamic degree $d_p$ with only one eigenvalue of maximal modulus. Let $\mu$ be its equilibrium measure. In this paper, we prove that $\mu$ is exponentially mixing for all d.s.h.\ test functions.

We study the global dynamics of holomorphic correspondences [Formula: see text] on a compact Riemann surface [Formula: see text] in the case, so far not well understood, where [Formula: see text] and [Formula: see text] have the same topological degree. In the absence of a mild and necessary obstruction that we call weak modularity, [Formula: see t...

Let $f$ be a H\'enon-Sibony map (regular polynomial automorphism) of $\mathbb{C}^k$ and let $\mu$ be the equilibrium measure of $f$. In this paper we prove that $\mu$ is exponentially mixing for plurisubharmonic test functions.

We study random products of matrices in SL 2 (C) from the point of view of holomorphic dynamics. For non-elementary measures with finite first moment we obtain the exponential convergence towards the stationary measure in Sobolev norm. As a consequence we obtain the exponentially fast equidistribution of forward images of points towards the station...

We study the dynamics of holomorphic correspondences f on a compact Riemann surface X in the case, so far not well understood, where f and f^−1 have the same topological degree. Under a mild and necessary condition that we call non weak modu-larity, f admits two canonical probability measures µ + and µ − which are invariant by f * and f * respectiv...