73 citations · 940 across the 53 of their papers we have counts for
3 papers · 1 filter
Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
Stefan Grosskinsky, Alexander A. Lovisolo, Daniel Ueltschi
We study random spatial permutations on Z^3 where each jump x -> π(x) is penalized by a factor exp(-T ||x-π(x)||^2). The system is known to exhibit a phase transition for low enoug…
Quantum Heisenberg models and their probabilistic representations
Christina Goldschmidt, Daniel Ueltschi, Peter Windridge
These notes give a mathematical introduction to two seemingly unrelated topics: (i) quantum spin systems and their cycle and loop representations, due to Tóth and Aizenman-Nachterg…
Cycle structure of random permutations with cycle weights
Nicholas M. Ercolani, Daniel Ueltschi
We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle…