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math.PR2025
A discontinuous percolation phase transition on the hierarchical lattice
Johannes Bäumler, Tom Hutchcroft
For long-range percolation on with translation-invariant edge kernel , it is a classical theorem of Aizenman and Newman (1986) that the phase transition is disconti…
math.PR2025
Permutations in competing growth processes and balls-in-bins
Johannes Bäumler, Tejas Iyer
Consider a model of independent, increasing -valued processes, with random, independent waiting times between jumps. It is known that there is either an emergent…
math.PR2025
Local criteria for global connectivity comparisons: beyond stochastic domination
Johannes Bäumler, Benedikt Jahnel, Jonas Köppl +3
We introduce a site-wise domination criterion for local percolation models, which enables the comparison of one-arm probabilities even in the absence of stochastic domination. The…