Ion Grama

activity

20242026

collaborators

16 papers

math.PR2026

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

Ion Grama, Jean-FranÃ§ois 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-FranÃ§ois 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.PR2026

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

Ion Grama, Jean-FranÃ§ois 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.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 $2 + I^´$ for some $Î…

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.PR2025

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…