11 papers
Large deviations for maximum local time of simple random walk in dimensions
Xinyi Li, Yushu Zheng
We obtain sharp asymptotic probabilities for upward deviations of the maximum local time of discrete- and continuous-time simple random walks on , . For downw…
Ultra-Confinement of Polaritons in Single Atomic Layer Ag Photonic Quantum Dots
Xinyi Li, Tetyana Ignatova, Chengye Dong +8
Light scattering by two-dimensional (2D) van der Waals heterostructures (vdWHs) is immense, especially given their infinitesimal volume, thus enabling strong light-matter interacti…
Tail exponents of the three-dimensional uniform spanning tree and Abelian sandpile
Xinyi Li, Runsheng Liu, Daisuke Shiraishi
We study the local geometry of the three-dimensional uniform spanning tree and its connection with the Abelian sandpile model. We obtain sharp tail exponents, up to subpolynomial e…
Generalized intersection exponents and local cut points for three-dimensional Brownian loop soup
Yifan Gao, Ruixuan Li, Xinyi Li
We study generalized non-intersection probabilities for the three-dimensional Brownian loop soup at subcritical intensities. We establish the existence of generalized intersection…
On a Conjecture about Sums Involving Farey Fractions
Anji Dong, Xinyi Li, Vi Anh Nguyen
In this paper, we prove a conjecture by Daniele Mundici on the sum of squared distances between consecutive elements in the -th Farey sequence for and …
Favorite sites for simple random walk in two and more dimensions
Chenxu Hao, Xinyi Li, Izumi Okada +1
On the trace of a discrete-time simple random walk on for , we consider the evolution of favorite sites, i.e., sites that achieve the maximal local time at…