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math.PR2021★ 1 cited
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…
math.PR2020★ 5 cited
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…
math.PR2019
The Surprising Accuracy of Benford's Law in Mathematics
Zhaodong Cai, Matthew Faust, A. J. Hildebrand +2
Benford's law is an empirical ``law'' governing the frequency of leading digits in numerical data sets. Surprisingly, for mathematical sequences the predictions derived from it can…