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math.PR2024
Spectral non-concentration near the top for unimodular random graphs
Mikolaj Fraczyk, Ben Hayes, Madhu Sudan +1
In recent work on equiangular lines, Jiang, Tidor, Yuan, Zhang, and Zhao showed that a connected bounded degree graph has sublinear second eigenvalue multiplicity. More generally t…
math.PR2023
Growth dichotomy for unimodular random rooted trees
Miklós Abert, Mikołaj Frączyk, Ben Hayes
We show that the growth of a unimodular random rooted tree of degree bounded by always exists, assuming its upper growth passes the critical threshold . Thi…