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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
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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