9 papers
Finite- and long-range spin-wave free-energy asymptotics for the two-dimensional quantum Heisenberg ferromagnet
Andreas Klippel
For the two-dimensional quantum Heisenberg ferromagnet with asymptotically radial power-law exchange, we prove the leading low-temperature free energy at every fixed spin, uniforml…
Infinite-mean Galton-Watson trees have zero random-interchange threshold
Andreas Klippel, Benjamin Lees, Christian Mönch
We prove that, on a Galton-Watson tree with almost surely finite offspring and infinite offspring mean, the random interchange process has critical parameter zero for infinite cycl…
Critical-curve regularity for finite-lifespan frog models via local-to-global comparisons
Christian Mönch, Andreas Klippel
We study the phase boundary of the finite-lifespan frog model. For rate-one continuous-time simple random walk on an infinite, connected, locally finite transitive graph of superli…
Dimer model and random lattice permutations with general weights
Andreas Klippel, Lorenzo Taggi, Wei Wu
The dimer model and random lattice permutations are two fundamental objects at the interface of probability, combinatorics, and mathematical physics. We study these models on finit…
Free-Energy Asymptotics of the Two-Dimensional Quantum Heisenberg Ferromagnet
Andreas Klippel
We prove the leading low-temperature free-energy asymptotics of the nearest-neighbour quantum Heisenberg ferromagnet on . For every fixed $S\in\{\frac12,1,\frac32,\ldo…
(Non-)coincidence of critical parameters for Poisson Zoos and Loop Soup Percolation on , , and ,
Volker Betz, Alexander Drewitz, Andreas Klippel +1
In this article we investigate the (non)-coincidence of critical parameters for various related percolation problems. More precisely, for the random walk loop soup we show that on…
Macroscopic loops in the random loop model on sparse random graphs
Andreas Klippel
We study the random loop model with crosses and bars on sparse random graphs. Our main objective is to prove the existence of macroscopic loops, in the sense that a loop visits a p…
Extremes of the zero-average Gaussian Free Field on random regular graphs
Lisa Hartung, Andreas Klippel, Christian Mönch
We study the extreme value statistics of the zero-average Gaussian free field (GFF) on random -regular graphs and the Gaussian free field on -regular trees. For random -re…
Loop vs. Bernoulli percolation on trees: strict inequality of critical values
Andreas Klippel, Benjamin Lees, Christian Mönch
We study loop ensembles on locally finite rooted trees. The loops are induced by a Poisson process of links on the edges; the transposition-only case is the random interchange proc…