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math.PR2025
The Uniform Random Walk on graphs, loop processes and graphings
Miklos Abert, Adam Arras, Jaelin Kim
We define the Uniform Random Walk (URW) on a connected, locally finite graph as the weak limit of the uniform walk of length starting at a fixed vertex. When the limit exists,…
math.PR2025
Random Schrödinger operators and convolution on wreath products
Adam Arras
We establish a spectral correspondence between random Schrödinger operators and deterministic convolution operators on wreath products, generalizing previous results that relate La…