Matthew Jenssen

activity

20152026

most citedOn the average size of independent sets in triangle-free graphs

41 citations · 162 across the 24 of their papers we have counts for

collaborators

Showing math.PRShow all

8 papers · 1 filter

math.PR2026

On the self-intersection time of non-backtracking random walks

Ferenc Bencs, Leslie Ann Goldberg, Matthew Jenssen +4

We study the self-intersection time of the non-backtracking random walk on connected undirected graphs. For every fixed $Δ \geq 3$ we show that the expected self-intersection time i…

math.PR2026

A simple proof of rapid mixing on random regular graphs beyond uniqueness

Andreas Göbel, Matthew Jenssen, Marcus Michelen +3

A recent breakthrough of Chen, Chen, Chen, Yin, and Zhang shows rapid mixing for Glauber dynamics for the hard-core model on random regular graphs beyond the tree uniqueness thresh…

math.PR2024★ 1 cited

Lower tails for triangles inside the critical window

Matthew Jenssen, Will Perkins, Aditya Potukuchi +1

We study the probability that the random graph $G (n, p)$ is triangle-free. When $p = o (n^{- 1/2})$ or $p = ω (n^{- 1/2})$ the asymptotics of the logarithm of this probability are known…

math.PR2022

The least singular value of a random symmetric matrix

Marcelo Campos, Matthew Jenssen, Marcus Michelen +1

Let $A$ be a $n \times n$ symmetric matrix with $(A_{i, j})_{i \leq j}$ , independent and identically distributed according to a subgaussian distribution. We show that $$\mathbb{P}(σ…

math.PR2021★ 1 cited

The singularity probability of a random symmetric matrix is exponentially small

Marcelo Campos, Matthew Jenssen, Marcus Michelen +1

Let $A$ be drawn uniformly at random from the set of all $n \times n$ symmetric matrices with entries in ${- 1, 1}$ . We show that \[ \mathbb{P}( \det(A) = 0 ) \leq e^{-cn},\] where…

math.PR2020

Singularity of random symmetric matrices revisited

Marcelo Campos, Matthew Jenssen, Marcus Michelen +1

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 $exp (- c (n lo g n)^{1/2})$ , which repre…

math.PR2020★ 2 cited

Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs

Tyler Helmuth, Matthew Jenssen, Will Perkins

For $Δ \geq 5$ and $q$ large as a function of $Δ$ , we give a detailed picture of the phase transition of the random cluster model on random $Δ$ -regular graphs. In particular, we dete…

math.PR2017★ 32 cited

On the hard sphere model and sphere packings in high dimensions

Matthew Jenssen, Felix Joos, Will Perkins

We prove a lower bound on the entropy of sphere packings of $R^{d}$ of density $Θ (d \cdot 2^{- d})$ . The entropy measures how plentiful such packings are, and our result is si…