Christopher D. Sinclair

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20242026

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math-ph2026

Exact Solvability via the KP Hierarchy for $β = L^{2}$ Random Matrix Ensembles

Christopher D. Sinclair

Random matrix ensembles with Dyson index $β = L^{2}$ describe systems of $M$ charge- $L$ particles interacting logarithmically in the presence of an external potential, yet exact form…

math-ph2025

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer

Christopher D. Sinclair, Jonathan M. Wells

We give a hyperpfaffian formulation for correlation functions in $β$ -ensembles arising in random matrix theory and statistical mechanics when $β = L^{2}$ is an even square integer. Mo…

math-ph2024

Electrostatics on Branching Processes

Christopher D. Sinclair

We introduce a random probability measure on the profinite completion of the random tree of a branching process and introduce the canonical and grand canonical ensembles of random…

Exact Solvability via the KP Hierarchy for β=L2 Random Matrix Ensembles

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer

Electrostatics on Branching Processes

Exact Solvability via the KP Hierarchy for $β = L^{2}$ Random Matrix Ensembles