Konstantin Tikhomirov

activity

20122024

most citedThe smallest singular value of random rectangular matrices with no moment assumptions on entries

1 citations · 1 across the 5 of their papers we have counts for

collaborators

Showing math.PRShow all

4 papers · 1 filter

math.PR2024

A note on the capacity of the binary perceptron

Dylan J. Altschuler, Konstantin Tikhomirov

Determining the capacity $α_{c}$ of the Binary Perceptron is a long-standing problem. Krauth and Mezard (1989) conjectured an explicit value of $α_{c}$ , approximately equal to .833, an…

math.PR2023

On pseudospectrum of inhomogeneous non-Hermitian random matrices

Konstantin Tikhomirov

Let $A$ be an $n \times n$ matrix with mutually independent centered Gaussian entries. Define \begin{align*} σ^*:=\max\limits_{i,j\leq n}\sqrt{{\mathbb E}\,|A_{i,j}|^2}, \quad σ:=\m…

math.PR2014

The limit of the smallest singular value of random matrices with i.i.d. entries

Konstantin Tikhomirov

Let ${a_{ij}}$ $(1 \leq i, j < \infty)$ be i.i.d. real valued random variables with zero mean and unit variance and let an integer sequence $(N_{m})_{m = 1}^{\infty}$ satisfy $m/N_m\longrig…

math.PR2014★ 1 cited

The smallest singular value of random rectangular matrices with no moment assumptions on entries

Konstantin E. Tikhomirov

Let $δ > 1$ and $β > 0$ be some real numbers. We prove that there are positive $u, v, N_{0}$ depending only on $β$ and $δ$ with the following property: for any $N, n$ such that $N\ge \max(N…