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Probability and Dynamical Systems Seminar
Probability and Dynamical Systems Seminar
Maximal Gaps for Dilated Lacunary Sequences
Maximal Gaps for Dilated Lacunary Sequences
Organizers
Speaker
Bohan Yang
Time
Tuesday, June 23, 2026 3:15 PM - 4:15 PM
Venue
A3-3-301
Online
Zoom 482 240 1589
(BIMSA)
Abstract
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.
Speaker Intro
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.