Maximal Gaps for Dilated Lacunary Sequences
演讲者
Bohan Yang
时间
2026年06月23日 15:15 至 16:15
地点
A3-3-301
线上
Zoom 482 240 1589
(BIMSA)
摘要
Let \((a_n)_{n\ge1}\subset\mathbb N\) be a lacunary sequence, \(a_{n+1}\ge q a_n\) for \(q>1\). For \(x\in\mathbb T\), we study the maximal empty circular gap $G_N\ (x)$ of the finite orbit \(\{a_1\ x,\ldots,a_N \ x\}\). We prove that, for Lebesgue-almost every $x$,
$$
\qquad \qquad \qquad \frac{1}{2} \le \liminf_{N\to\infty}\frac{N \ G_N\ \ (x)}{\log N}\le \limsup_{N\to\infty}\frac{N \ G_N\ \ (x)}{\log N}\le 1+\frac{2}{q-1}.
$$
We further establish analogous almost-sure estimates for lacunary sequences with real values, and develop higher-dimensional extensions for the maximal convex gaps. This is joint work with Yuval Peres.
$$
\qquad \qquad \qquad \frac{1}{2} \le \liminf_{N\to\infty}\frac{N \ G_N\ \ (x)}{\log N}\le \limsup_{N\to\infty}\frac{N \ G_N\ \ (x)}{\log N}\le 1+\frac{2}{q-1}.
$$
We further establish analogous almost-sure estimates for lacunary sequences with real values, and develop higher-dimensional extensions for the maximal convex gaps. This is joint work with Yuval Peres.
演讲者介绍
Bohan Yang is a postdoctoral researcher at the Shanghai Institute of Mathematics and Interdisciplinary Sciences (SIMIS). He obtained a Doctor of Mathematics degree from Tsinghua University in 2025. His main research interests include homogeneous dynamics, Teichmüller dynamics, and their applications in number theory.