Tianyi Bai

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math.PR2026

Critical branching random walks on $Z^{2}$ : local survival probabilities and Yaglom limit theorems

Tianyi Bai, Xinxin Chen, Shen Lin

We consider a branching random walk on $Z^{2}$ with critical offspring of mean $1$ and spatial motion governed by the jumps of a lazy simple random walk. For every site $x\i…

math.PR2024

Minkowski sum of fractal percolation and random sets

Tianyi Bai, Xinxin Chen, Yuval Peres

In this paper, we prove that hitting probability of Minkowski sum of fractal percolations can be characterized by capacity. Then we extend this result to Minkowski sum of general r…

math.PR2024

Proof of off-diagonal long-range order in a mean-field trapped Bose gas via the Feynman--Kac formula

Tianyi Bai, Wolfgang König, Quirin Vogel

We consider the non-interacting Bose gas of $N$ bosons in dimension $d \geq 3$ in a trap in a mean-field setting with a vanishing factor $a_{N}$ in front of the kinetic energy. The ch…

Critical branching random walks on Z2: local survival probabilities and Yaglom limit theorems

Minkowski sum of fractal percolation and random sets

Proof of off-diagonal long-range order in a mean-field trapped Bose gas via the Feynman--Kac formula

Critical branching random walks on $Z^{2}$ : local survival probabilities and Yaglom limit theorems