Shuxiong Zhang

activity

20202026

collaborators

11 papers

math.PR2026

A large-deviation principle for the empirical distribution of a regular branching random walk

Shuxiong Zhang, Yaping Zhu

Let $\{Z_n\}_{n\geq0}$ be a supercritical branching random walk with deterministic rooted $b$-ary tree, $b\geq2$, and symmetric displacements satisfying \(\lim_{x\to+\infty}x…

math.PR2025

On the maximal displacement of subcritical branching random walks with or without killing

Haojie Hou, Shuxiong Zhang

Consider a subcritical branching random walk ${Z_{k}}_{k \geq 0}$ with offspring distribution ${p_{k}}_{k \geq 0}$ and step size $X$ . Let $M_{n}$ denote the rightmost position reached…

math.PR2025

Beyond Poisson Approximation: Sums of Markovian Bernoulli Variables with Applications to Brownian Motions and Branching Processes

Hua-Ming Wang, Shuxiong Zhang

Let ${η_{i}}_{i \geq 1}$ be a sequence of dependent Bernoulli random variables. While the Poisson approximation for the distribution of $\sum_{i = 1}^{n} η_{i}$ has been extensively studied…

math.PR2025

On empty balls of critical 2-dimensional branching random walks

Shuxiong Zhang

Let ${Z_{n}}_{n \geq 0}$ be a critical $d$ -dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesgue measure on $R^{d}$ …

math.PR2024

Upper deviation probabilities for the range of a supercritical super-Brownian motion

Shuxiong Zhang

Let ${X_{t}}_{t \geq 0}$ be a $d$ -dimensional supercritical super-Brownian motion started from the origin with branching mechanism $ψ$ . Denote by $R_t:=\inf\{r>0:X_s(\{x\in \mathbb…

math.PR2024

Upper deviation probabilities for level sets of a supercritical branching random walk

Shuxiong Zhang, Lianghui Luo

Given a supercritical branching random walk ${Z_{n}}_{n \geq 0}$ on $R$ , let $Z_{n} ([y, \infty))$ be the number of particles located in $[y, \infty) \subset R$ at genera…

math.PR2022

On the empty balls of a critical or subcritical branching random walk

Jie Xiong, Shuxiong Zhang

Let ${Z_{n}}_{n \geq 0}$ be a critical or subcritical $d$ -dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure o…

math.PR2022

Large deviation probabilities for the range of a d-dimensional supercritical branching random walk

Shuxiong Zhang

Let ${Z_{n}}_{n \geq 0}$ be a $d$ -dimensional supercritical branching random walk started from the origin. Write $Z_{n} (S)$ for the number of particles located in a set $S\subset\mat…

math.PR2022

On the empty balls of a critical super-Brownian motion

Jie Xiong, Shuxiong Zhang

Let ${X_{t}}_{t \geq 0}$ be a $d$ -dimensional critical super-Brownian motion started from a Poisson random measure whose intensity is the Lebesgue measure. Denote by $R_t:=\sup\{u>0:…

math.PR2020

Lower deviation probabilities for level sets of the branching random walk

Shuxiong Zhang

Given a branching random walk ${Z_{n}}_{n \geq 0}$ on $R$ , let $Z_{n} ([y, \infty))$ be the number of particles located in $[y, \infty)$ at generation $n$ . It is known from \cite{…

math.PR2020

On large deviation probabilities for empirical distribution of branching random walks with heavy tails

Shuxiong Zhang

Given a branching random walk $(Z_{n})_{n \geq 0}$ on $R$ , let $Z_{n} (A)$ be the number of particles located in interval $A$ at generation $n$ . It is well known (e.g., \cite{big…