5 citations · 14 across the 10 of their papers we have counts for
10 papers
The Conclave Process
Itai Benjamini, Zhenhao Cai, Guanyi Chen +2
We introduce a stochastic model for the papal conclave in which cardinals vote repeatedly among themselves until one cardinal receives all the votes. In each round, the probabi…
Asymptotics for the percolation threshold of finitary random interlacements in four and higher dimensions
Yijie Bi, Zhenhao Cai, Xinyi Li +2
We establish sharp asymptotic bounds for the critical intensity of the Finitary Random Interlacements (FRI) model in four and higher dimensions with general trajectory length distr…
Minimal harmonic measure on 2D lattices
Zhenhao Cai, Eviatar B. Procaccia, Yuan Zhang
We study the harmonic measure (i.e. the limit of the hitting distribution of a simple random walk starting from a distant point) on three canonical two-dimensional lattices: the sq…
Vertex-removal stability and the least positive value of harmonic measures
Zhenhao Cai, Gady Kozma, Eviatar B. Procaccia +1
We prove that for (), the vertex-removal stability of harmonic measures (i.e. it is feasible to remove some vertex while changing the harmonic measure by a b…
One-arm exponent of critical level-set for metric graph Gaussian free field in high dimensions
Zhenhao Cai, Jian Ding
In this paper, we study the critical level-set of Gaussian free field (GFF) on the metric graph . We prove that the one-arm probability (i.e. the prob…
On the exact orders of critical value in Finitary Random Interlacements
Zhenhao Cai, Yuan Zhang
In this paper, we prove the exact orders of critical intensity in Finitary Random Interlacements (FRI) in with respect to the expected fiber lengt…
Continuity and uniqueness of percolation critical parameters in Finitary Random Interlacements
Zhenhao Cai, Eviatar B. Procaccia, Yuan Zhang
We prove that the critical percolation parameter for Finitary Random Interlacements (FRI) is continuous with respect to the path length parameter . The proof uses a result which…
Some Rigorous Results on the Phase Transition of Finitary Random Interlacement
Zhenhao Cai, Yuan Zhang
In this paper, we show several rigorous results on the phase transition of Finitary Random Interlacement (FRI). For the high intensity regime, we show the existence of a critical f…
On (non-)monotonicity and phase diagram of finitary random interlacement
Zhenhao Cai, Yunfeng Xiong, Yuan Zhang
In this paper, we study the evolution of a Finitary Random Interlacement (FRI) with respect to the expected length of each fiber. In contrast to the previously proved phase transit…
On Chemical Distance and Local Uniqueness of a Sufficiently Supercritical Finitary Random Interlacement
Zhenhao Cai, Xiao Han, Jiayan Ye +1
In this paper, we study geometric properties of the unique infinite cluster in a sufficiently supercritical Finitary Random Interlacements in $\mathbb{Z}^d…