170 citations · 523 across the 31 of their papers we have counts for
8 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…
The density of states of 1D random band matrices via a supersymmetric transfer operator
Margherita Disertori, Martin Lohmann, Sasha Sodin
Recently, T. and M. Shcherbina proved a pointwise semicircle law for the density of states of one-dimensional Gaussian band matrices of large bandwidth. The main step of their proo…
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…
A supersymmetric approach to martingales related to the vertex-reinforced jump process
Margherita Disertori, Franz Merkl, Silke W. W. Rolles
Sabot and Zeng have discovered two martingales, one of which played a key role in their investigation of the vertex-reinforced jump process. Starting from the related supersymmetri…