Hui Xiao

activity

20172026

most citedA zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group

13 citations · 53 across the 20 of their papers we have counts for

collaborators

23 papers

math.PR2026

On the tails of the invariant measure for multidimensional affine stochastic recursions in the critical case

Ion Grama, Sebastian Mentemeier, Hui Xiao

We study the behavior at infinity of the invariant Radon measure for the multidimensional affine stochastic recursion $V_{n} = A_{n} V_{n - 1} + B_{n},$ where $(A_{n})_{n \geq 1}$ are positi…

math.PR2026

Local limit theorem for the operator norm of products of random matrices

Ion Grama, Jean-François Quint, Hui Xiao

We prove a local limit theorem for the quantity $∥ g_{n} \dots g_{1} ∥$ , where $g_{1}, g_{2}, \dots$ is a sequence of independent and identically distributed random invertible square m…

math.GR2026

Strong non-arithmeticity for Zariski dense subsemigroups

Ion Grama, Jean-François Quint, Hui Xiao

We prove a non-arithmeticity property for the complex eigenvalues of a Zariski dense subsemigroups of real reductive algebraic groups. This property will be used in [7] in order to…

math.PR2025

Local limit theorems for conditioned random walks by the heat kernel approximation

Ion Grama, Hui Xiao

We study the random walk $(S_{n})_{n \geq 1}$ with independent and identically distributed real-valued increments having zero mean and an absolute moment of order $2 + δ$ for some $δ>…

math.PR2025

Spinal decomposition, martingale convergence and the Seneta-Heyde scaling for matrix branching random walks

Ion Grama, Sebastian Mentemeier, Hui Xiao

We consider a matrix branching random walk on the semi-group of nonnegative matrices, where we are able to derive, under general assumptions, an analogue of Biggins' martingale con…

math.PR2024

Gaussian heat kernel asymptotics for conditioned random walks

Ion Grama, Hui Xiao

Consider a random walk $S_{n} = \sum_{i = 1}^{n} X_{i}$ with independent and identically distributed real-valued increments with zero mean, finite variance and moment of order $2 + δ$ for so…

math.PR2024

Conditioned random walks on linear groups II: local limit theorems

Ion Grama, Jean-François Quint, Hui Xiao

We investigate random walks on the general linear group constrained within a specific domain, with a focus on their asymptotic behavior. In a previous work [38], we constructed the…

math.PR2024

Conditioned random walks on linear groups I: construction of the target harmonic measure

Ion Grama, Jean-François Quint, Hui Xiao

Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. Th…

math.PR2023

Conditioned local limit theorems for products of positive random matrices

Ion Grama, Hui Xiao

Let $(g_{n})_{n \geq 1}$ be a sequence of independent and identically distributed positive random $d \times d$ matrices, where $d \geq 2$ is an integer. For any starting point $x \in…

math.PR2023

Limit theorems for first passage times of multivariate perpetuity sequences

Sebastian Mentemeier, Hui Xiao

We study the first passage time $τ_{u} = in f {n \geq 1 : ∣ V_{n} ∣ > u}$ for the multivariate perpetuity sequence $V_{n} = Q_{1} + M_{1} Q_{2} + \dots + (M_{1} \dots M_{n - 1}) Q_{n}$ , where $(M…

math.PR2022★ 1 cited

Moderate deviations and local limit theorems for the coefficients of random walks on the general linear group

Hui Xiao, Ion Grama, Quansheng Liu

Consider the random walk $G_{n} := g_{n} \dots g_{1}$ , $n \geq 1$ , where $(g_{n})_{n \geq 1}$ is a sequence of independent and identically distributed random elements with law $μ$ on the…

math.PR2022★ 2 cited

Edgeworth expansion for the coefficients of random walks on the general linear group

Hui Xiao, Ion Grama, Quansheng Liu

Let $(g_{n})_{n \geq 1}$ be a sequence of independent and identically distributed random elements with law $μ$ on the general linear group $GL (V)$ , where $V = R^{d}$ . Con…

math.PR2022

Edgeworth expansion and large deviations for the coefficients of products of positive random matrices

Hui Xiao, Ion Grama, Quansheng Liu

Consider the matrix products $G_{n} := g_{n} \dots g_{1}$ , where $(g_{n})_{n \geq 1}$ is a sequence of independent and identically distributed positive random $d \times d$ matrices. Under…

math.PR2022★ 1 cited

The extremal position of a branching random walk on the general linear group

Ion Grama, Sebastian Mentemeier, Hui Xiao

Consider a branching random walk $(G_{u})_{u \in T}$ on the general linear group $GL (V)$ of a finite dimensional space $V$ , where $T$ is the associated geneal…

math.PR2021★ 3 cited

Limit theorems for the coefficients of random walks on the general linear group

Hui Xiao, Ion Grama, Quansheng Liu

Let $(g_{n})_{n \geq 1}$ be a sequence of independent and identically distributed random elements with law $μ$ on the general linear group $GL (V)$ , where $V = R^{d}$ . Con…

math.DS2021★ 3 cited

Conditioned limit theorems for hyperbolic dynamical systems

Ion Grama, Jean-François Quint, Hui Xiao

Let $(X, T)$ be a subshift of finite type equipped with the Gibbs measure $ν$ and let $f$ be a real-valued Hölder continuous function on $X$ such that $ν (f) = 0$ . C…

math.PR2021★ 6 cited

Conditioned local limit theorems for random walks on the real line

Ion Grama, Hui Xiao

Consider a random walk $S_{n} = \sum_{i = 1}^{n} X_{i}$ with independent and identically distributed real-valued increments $X_{i}$ of zero mean and finite variance. Assume that $X_{i}$ is non-l…

math.PR2020★ 6 cited

Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

Hui Xiao, Ion Grama, Quansheng Liu

Let $(g_{n})_{n \geq 1}$ be a sequence of independent and identically distributed positive random $d \times d$ matrices and consider the matrix product $G_{n} := g_{n} \dots g_{1}$ . Under…

math.PR2020★ 7 cited

Large deviation expansions for the coefficients of random walks on the general linear group

Hui Xiao, Ion Grama, Quansheng Liu

Let $(g_{n})_{n \geq 1}$ be a sequence of independent and identically distributed elements of the general linear group $G L (d, R)$ . Consider the random walk $G_n: = g_n \ldots…

math.PR2020★ 13 cited

A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group

Ion Grama, Jean-François Quint, Hui Xiao

We prove a zero-one law for the stationary measure for algebraic sets generalizing the results of Furstenberg [13] and Guivarc'h and Le Page [20]. As an application, we establish a…

math.PR2019

Precise large deviation asymptotics for products of random matrices

Hui Xiao, Ion Grama, Quansheng Liu

Let $(g_{n})_{n \geq 1}$ be a sequence of independent identically distributed $d \times d$ real random matrices with Lyapunov exponent $γ$ . For any starting point $x$ on the unit sph…

math.PR2019★ 3 cited

Berry-Esseen bound and precise moderate deviations for products of random matrices

Hui Xiao, Ion Grama, Quansheng Liu

Let $(g_{n})_{n \geq 1}$ be a sequence of independent and identically distributed (i.i.d.) $d \times d$ real random matrices. For $n \geq 1$ set $G_{n} = g_{n} \dots g_{1}$ . Given any star…

math.PR2017★ 8 cited

Averaging principle for one dimensional stochastic Burgers equation

Zhao Dong, Xiaobin Sun, Hui Xiao +1

In this paper, we consider the averaging principle for one dimensional stochastic Burgers equation with slow and fast time-scales. Under some suitable conditions, we show that the…