3 papers
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.PR2018
Uniqueness and Non-Uniqueness for Spin-Glass Ground States on Trees
Johannes Bäumler
We consider a Spin Glass at temperature where the underlying graph is a locally finite tree. We prove for a wide range of coupling distributions that uniqueness of ground s…