Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Julian Sahasrabudhe"'
Publikováno v:
Forum of Mathematics, Pi, Vol 12 (2024)
Let A be an $n \times n$ symmetric matrix with $(A_{i,j})_{i\leqslant j}$ independent and identically distributed according to a subgaussian distribution. We show that $$ \begin{align*}\mathbb{P}(\sigma_{\min}(A) \leqslant \varepsilon n^{-1/2}
Externí odkaz:
https://doaj.org/article/27ea596492494fdd9fc776b3299d8a5a
Autor:
Marcus Michelen, Julian Sahasrabudhe
Publikováno v:
Discrete Analysis (2022)
Anti-concentration of random variables from zero-free regions, Discrete Analysis 2022:13, 29 pp. In recent years there have been a number of breakthroughs concerning the probability that a random matrix is singular. There are several natural notions
Externí odkaz:
https://doaj.org/article/33231dc5330345a49c6b26b92d15b23b
Autor:
Marcus Michelen, Julian Sahasrabudhe
Publikováno v:
Discrete Analysis (2020)
A characterization of polynomials whose high powers have non-negative coefficients, Discrete Analysis 2020:20, 16 pp. Polynomials with non-negative coefficients are an important class of polynomials that appear in many contexts. This paper character
Externí odkaz:
https://doaj.org/article/669495ca79ff45a08383f6baf8868246
Publikováno v:
Proceedings of the American Mathematical Society. 150:3147-3159
Let $M_n$ be drawn uniformly from all $\pm 1$ symmetric $n \times n$ matrices. We show that the probability that $M_n$ is singular is at most $\exp(-c(n\log n)^{1/2})$, which represents a natural barrier in recent approaches to this problem. In addit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4accaf2b6d34989b3e2828373b3e6f39
https://doi.org/10.1090/proc/15807
https://doi.org/10.1090/proc/15807
Publikováno v:
Inventiones mathematicae. 228:377-414
Since their introduction by Erdős in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and numerous questions and conjectures have been posed regarding the existenc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::307813746ef90af36b4edb157f34ef69
https://doi.org/10.1007/s00222-021-01087-5
https://doi.org/10.1007/s00222-021-01087-5
Publikováno v:
Algebra & Number Theory. 15:609-626
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erd\H{o}s in 1950, and over the following decades numerous problems were posed
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29824fa894f5181d68eff027920773b9
https://doi.org/10.2140/ant.2021.15.609
https://doi.org/10.2140/ant.2021.15.609
Autor:
Tomas Juškevičius, Julian Sahasrabudhe
Publikováno v:
Bulletin of the London Mathematical Society, Hoboken : Wiley, 2021, vol. 53, iss. 3, p. 877-892
In a celebrated paper, Borwein, Erd\'elyi, Ferguson and Lockhart constructed cosine polynomials of the form \[ f_A(x) = \sum_{a \in A} \cos(ax), \] with $A\subseteq \mathbb{N}$, $|A|= n$ and as few as $n^{5/6+o(1)}$ zeros in $[0,2\pi]$, thereby dispr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1edd148fe961c5e258f956dd0d512371
https://doi.org/10.1112/blms.12468
https://doi.org/10.1112/blms.12468
Publikováno v:
Acta Mathematica Hungarica. 161:540-549
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erdős in 1950, and over the following decades he asked many questions about them. Most famously, he a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::54eaded90fb322b6a0af61976496e9b8
https://doi.org/10.1007/s10474-020-01048-z
https://doi.org/10.1007/s10474-020-01048-z
Publikováno v:
Acta Mathematica Hungarica. 161:197-200
In this short note we give a simple proof of a 1962 conjecture of Erdős, first proved in 1969 by Crittenden and Vanden Eynden, and note two corollaries.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c38379e25284b52088b3317aa70ffd93
https://doi.org/10.1007/s10474-019-00980-z
https://doi.org/10.1007/s10474-019-00980-z
Publikováno v:
Discrete Applied Mathematics. 260:66-74
For a constant γ ∈ [ 0 , 1 ] and a graph G , let ω γ ( G ) be the largest integer k for which there exists a k -vertex subgraph of G with at least γ k 2 edges. We show that if 0 p γ 1 then ω γ ( G n , p ) is concentrated on a set of two inte
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94d58b855527f43bf1c430351bcf61dd
https://doi.org/10.1016/j.dam.2019.01.032
https://doi.org/10.1016/j.dam.2019.01.032