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The Burton-Pemantle Theorem
A summmary proof that the uniform spanning tree on a graph is a determinantal process, with the explicit derivation of the kernel. The proof presented is originally due to Benjamini-Lyons-Peres-Schramm
Jan 9, 2022
Notes on Hamiltonian Systems
Notes on Hamiltonian Systems, by Tom Alberts
Oct 4, 2021
Cauchy Determinant Formula
Main Result This note is about Cauchy matrices of the form $$ M = M(\mathbf{a}, \mathbf{b}) = \left( \frac{1}{a_i - b_j} \right)_{1 \leq i, j \leq n} $$ where $\mathbf{a}, \mathbf{b} \in \mathbb{C}^n$.
Tom Alberts
Feb 25, 2022
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