5 papers
Log-concavity and concentration bounds for a single gap between GUE eigenvalues
Samuel G. G. Johnston
We observe that the distribution of the eigenvalues of an -by- GUE random matrix is log-concave on , and that the same is true for the law of a single gap betwe…
Explicit correlation functions for the six-vertex model in the free-fermion regime
Samuel G. G. Johnston, Rohan Shiatis
In this article, we show that, in the free-fermion regime of the six-vertex model, all -point correlation functions of vertex types admit a determinantal representation: \begin{…
On creating convexity in high dimensions
Samuel G. G. Johnston
Given a subset of , we define \begin{align*} \mathrm{conv}_k(A) := \left\{ λ_1 s_1 + \cdots + λ_k s_k : λ_i \in [0,1], \sum_{i=1}^k λ_i = 1 , s_i \in A \right\} \…
The Integrable Snake Model
Samuel G. G. Johnston, Rohan Shiatis
A pure snake configuration is a bijection containing no two-cycles and such that for each we have $σ(x) \in \{ x , x+ \mathbf…
Free probability via entropic optimal transport
Octavio Arizmendi, Samuel G. G. Johnston
Let and be compactly supported probability measures on , and let denote their additive free convolution. We show that for all sufficiently large r…