72 citations · 200 across the 16 of their papers we have counts for
14 papers · 1 filter
Restrictions of some reinforced processes to subgraphs
Margherita Disertori, Franz Merkl, Silke W. W. Rolles
We prove that the restriction of the vertex-reinforced jump process to a subset of the vertex set is a mixture of vertex-reinforced jump processes. A similar statement holds for th…
Transience of vertex-reinforced jump processes with long-range jumps
Margherita Disertori, Franz Merkl, Silke W. W. Rolles
We show that the vertex-reinforced jump process on the -dimensional lattice with long-range jumps is transient in any dimension as long as the initial weights do not decay t…
The non-linear supersymmetric hyperbolic sigma model on a complete graph with hierarchical interactions
Margherita Disertori, Franz Merkl, Silke W. W. Rolles
We study the non-linear supersymmetric hyperbolic sigma model on a complete graph with hierarchical interactions. For interactions which do not decrease too fast in the h…
Variance of voltages in a lattice Coulomb gas
Diana Conache, Markus Heydenreich, Franz Merkl +1
We study the behavior of the variance of the difference of energies for putting an additional electric unit charge at two different locations in the two-dimensional lattice Coulomb…
Random interlacements for vertex-reinforced jump processes
Franz Merkl, Silke W. W. Rolles, Pierre Tarrès
We introduce random interlacements for transient vertex-reinforced jump processes on a general graph . Using increasing finite subgraphs of with wired boundary conditi…
Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model
Margherita Disertori, Franz Merkl, Silke W. W. Rolles
We introduce a family of real random variables arising from the supersymmetric nonlinear sigma model and containing the family introduced by Sabot, Tarrès, and Zeng [ST…