Related papers: Sharp Favard length of random Cantor sets

Folded Reed-Solomon (FRS) codes are variants of Reed-Solomon codes, known for their optimal list decoding radius. We show explicit FRS codes with rate $R$ that can be list decoded up to radius $1-R-\epsilon$ with lists of size…

We develop a thorough analytical study of the $O(1/N)$ correction to the spectrum of regular random graphs with $N \rightarrow \infty$ nodes. The finite size fluctuations of the resolvent are given in terms of a weighted series over the…

Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…

In this paper we consider fractal percolation random Cantor sets $E$ on the plane constructed with non-homogeneous probabilities. We focus on the case when the probabilities are large enough to guarantee that the almost sure dimension of…

We consider a continuous time random walk $X$ in random environment on $\Z^+$ such that its potential can be approximated by the function $V: \R^+\to \R$ given by $V(x)=\sig W(x) -\frac{b}{1-\alf}x^{1-\alf}$ where $\sig W$ a Brownian motion…

This paper has two parts, on Baumslag-Solitar groups and on general G-trees. In the first part we establish bounds for stable commutator length (scl) in Baumslag-Solitar groups. For a certain class of elements, we further show that scl is…

Over the past years, operator splitting methods have become ubiquitous for non-smooth optimization owing to their simplicity and efficiency. In this paper, we consider the Forward--Douglas--Rachford splitting method (FDR) [10,40], and study…

This work extends Favard-type spectral representations for banded matrices $T$ beyond the bounded setting. It assumes that, for every $N\in\mathbb N_0$, there exists a shift $s_N\ge 0$ such that the shifted truncation $A_N:= T^{[N]}+s_N…

We prove a list recovery guarantee for random low-rate linear codes over sufficiently large prime fields. For fixed dimension $d$, error fraction $\alpha$, and accuracy parameter $\varepsilon$, a random $d$-dimensional linear code $C…

We show that the uniform radius of spatial analyticity $\sigma(t)$ of solution at time $t$ for the fifth order KdV-BBM equation cannot decay faster than $1/t$ for large $t>0$, given initial data that is analytic with fixed radius…

This paper analyses stable commutator length in groups Z^r * Z^s. We bound scl from above in terms of the reduced wordlength (sharply in the limit) and from below in terms of the answer to an associated subset-sum type problem. Combining…

We consider the statistical deconvolution problem where one observes $n$ replications from the model $Y=X+\epsilon$, where $X$ is the unobserved random signal of interest and $\epsilon$ is an independent random error with distribution…

We consider random trigonometric polynomials of the form \[ f_n(x,y)=\sum_{1\le k,l \le n} a_{k,l} \cos(kx) \cos(ly), \] where the entries $(a_{k,l})_{k,l\ge 1}$ are i.i.d. random variables that are centered with unit variance. We…

The power spectrum of magnetic-field fluctuations in the fast solar wind ($V_{\rm SW}> 500 \mbox{ km} \mbox{ s}^{-1}$) at magnetohydrodynamic (MHD) scales is characterized by two different power laws on either side of a break frequency…

The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…

Deterministic and random fractals, within the framework of Iterated Function Systems, have been used to model and study a wide range of phenomena across many areas of science and technology. However, for many applications deterministic…

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that…

Folded Reed-Solomon (FRS) codes are a well-studied family of codes, known for achieving list decoding capacity. In this work, we give improved deterministic and randomized algorithms for list decoding FRS codes of rate $R$ up to radius…

An $(r, s)$-formation is a concatenation of $s$ permutations of $r$ letters. If $u$ is a sequence with $r$ distinct letters, then let $\mathit{Ex}(u, n)$ be the maximum length of any $r$-sparse sequence with $n$ distinct letters which has…

Expander (Tanner) codes combine sparse graphs with local constraints, enabling linear-time decoding and asymptotically good distance--rate tradeoffs. A standard constraint-counting argument yields the global-rate lower bound $R\ge 2r-1$ for…