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math.PR2026
The critical activation density in graph bootstrap percolation
Brett Kolesnik, Tamás Makai, Tamás Makai +6
In graph bootstrap percolation, edges of an Erdős-Rényi random graph are initially active, and activation spreads to other edges of via the combinatorics…
math.PR2026
The stochastic block model has the overlap graph property for modularity
Shankar Bhamidi, David Gamarnik, Remco van der Hofstad +4
The overlap gap property (OGP) is a statement about the geometry of near-optimal solutions. Exhibiting OGP implies failure of a class of local algorithms; and has been observed to…
math.PR2025
Direct Paths in the Temporal Hypercube
Austin Eide, Martijn Gösgens, PaweÅ PraÅat
We consider the -dimensional random temporal hypercube, i.e., the -dimensional hypercube graph with its edges endowed with i.i.d. continuous random weights. We say that a ver…