Fourier-Walsh coefficients for a coalescing flow (discrete time)

Scaling limit of Fourier-Walsh coefficients (a framework)

Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.

随机 Fourier-Walsh 矩阵乘积的谱范数界

Spectral norm bound for the product of random Fourier-Walsh matrices

本文研究了归一化随机 Fourier-Walsh 矩阵乘积的谱范数界，在维数趋于无穷且期望矩阵乘积算子范数趋于零时，识别出一种有趣的多项式缩放机制。

低次傅里叶阈值用于随机布尔函数

Low-Degree Fourier Threshold for Random Boolean Functions

研究随机布尔函数是否由其度数不超过d的瓦尔什-傅里叶系数决定，证明阈值在p/2附近存在O(√(p log p))窗口，确定函数唯一性条件。

Stochastic flows and an interface SDE on metric graphs

This paper consists in the study of a stochastic differential equation on a metric graph, called an interface SDE $(\hbox{ISDE})$. To each edge of the graph is associated an independent white noise, which drives $(\hbox{ISDE})$ on this edge. This produces an interface at each vertex of the graph. We first do our study on star graphs with $N\ge 2$ rays. The case $N=2$ corresponds to the perturbed Tanaka's equation recently studied by Prokaj \cite{MR18} and Le Jan-Raimond \cite{MR000} among others. It is proved that $(\hbox{ISDE})$ has a unique in law solution, which is a Walsh's Brownian motion…

Mandelbrot 级联的调和分析——在向量值鞅背景下

Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales

本文利用向量值鞅理论解决 MCCM 的 Fourier 维数难题，给出精确公式、Salem 判据、多项式 Rajchman 衰减、β=1/2 二阶相变及限制估计。

Restricted Isometry of Fourier Matrices and List Decodability of Random Linear Codes

We prove that a random linear code over F_q, with probability arbitrarily close to 1, is list decodable at radius (1-1/q-ε) with list size L=O(1/ε^2) and rate R=Ω_q(ε^2/(log^3(1/ε))). Up to the polylogarithmic factor in (1/ε) and constant factors depending on q, this matches the lower bound L=Ω_q(1/ε^2) for the list size and upper bound R=O_q(ε^2) for the rate. Previously only existence (and not abundance) of such codes was known for the special case q=2 (Guruswami, Håstad, Sudan and Zuckerman, 2002). In order to obtain our result, we employ a relaxed version of the well known Johnson bound on…