We study the length of cycles of random permutations drawn from the Mallows distribution.
Under this distribution, the probability of a permutation π∈S_n is proportional to q^inv(π) …

We study the length of cycles in the model of spatial random permutations in Euclidean
space. In this model, for given length L, density ρ ρ, dimension d and jump density φ φ, one …

We resolve a long-standing conjecture of Wilson (Ann. Appl. Probab. 14 (2004) 274–325),
reiterated by Oliveira (2016), asserting that the mixing time of the interchange process with …

We consider an extension of the interchange process on the complete graph, in which a
fraction of the transpositions are replaced by 'reversals'. The model is motivated by statistical …

We consider nearest neighbour spatial random permutations on \mathbbZ^d. In this case,
the energy of the system is proportional to the sum of all cycle lengths, and the system can …

We study a class of quantum spin systems in the mean-field setting of the complete graph.
For spin S= 1 2⁠, the model is the Heisenberg ferromagnet, and for general spin S∈ 1 2 …

We study a family of random permutation models on the Hamming graph H (2, n)(ie, the 2-
fold Cartesian product of complete graphs), containing the interchange process and the …

These notes describe several loop soup models and their {\it universal behaviour} in
dimensions greater or equal to 3. These loop models represent certain classical or quantum …

The interchange process is a random permutation model that was introduced as a way to
study the quantum Heisenberg model. For this model, progress had been made on some …

The interchange process on a finite graph is obtained by placing a particle on each vertex of
the graph, then at rate 1, selecting an edge uniformly at random and swapping the two …