Y. Zhang

activity

20192021

most citedThe Surprising Accuracy of Benford's Law in Mathematics

6 citations · 14 across the 9 of their papers we have counts for

collaborators

9 papers

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.CV2020★ 1 cited

Rigidity theorems by the logarithmic capacity

Robert Xin Dong, Yuan Zhang

In light of the Suita conjecture, we explore various rigidity phenomena concerning the Bergman kernel, logarithmic capacity, Green's function, and Euclidean distance and volume.

math.AP2020

A remark on optimal data spaces for classical solutions of $\partial ˉ$

Martino Fassina, Yifei Pan, Yuan Zhang

We study the minimal regularity required on the datum to guarantee the existence of classical $C^{1}$ solutions to the inhomogeneous Cauchy-Riemann equations on planar domains.

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.MG2020

Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers

Ya-min Yang, Yuan Zhang

Let $M_{t, v, r} (n, m)$ , $2 \leq m < n$ , be the collection of self-affine carpets with expanding matrix $\diag(n,m)$ which are totally disconnected, possessing vacant rows and wit…

math.CV2020

Uniform estimates for the canonical solution to the $\partial ˉ$ -equation on product domains

Robert Xin Dong, Yifei Pan, Yuan Zhang

We obtain uniform estimates for the canonical solution to $\partial ˉ u = f$ on the Cartesian product of bounded planar domains with $C^{2}$ boundaries, when $f$ is continuous up to…

math.DS2020

Tilings of convex polyhedral cones and topological properties of self-affine tiles

Ya-min Yang, Yuan Zhang

Let $a_{1}, \dots, a_{r}$ be vectors in a half-space of $R^{n}$ . We call $C = a_{1} R^{+} + \dots + a_{r} R^{+}$ a convex polyhedral con…

math.DS2020★ 1 cited

Characterization of complementing pairs of $(Z_{\geq 0})^{n}$

Hui Rao, Ya-min Yang, Yuan Zhang

Let $A, B, C$ be subsets of an abelian group $G$ . A pair $(A, B)$ is called a $C$ -pair if $A, B \subset C$ and $C$ is the direct sum of $A$ and $B$ . The $(Z_{\geq 0})$ -pairs are ch…

math.PR2019★ 6 cited

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…