45 citations · 173 across the 15 of their papers we have counts for
16 papers
Determinantal linear spanning forests
Adrien Kassel, Thierry Lévy
We introduce a determinantal linear process on the space of -forms over a weighted graph endowed with a unitary local system, which we call the determinantal linear spanning for…
Trace identities for quiver representations
Adrien Kassel, Thierry Lévy
We give an expression for the determinant of the twisted Laplacian associated with any linear representation of a finite quiver in terms of traces of the holonomy of its cycles. To…
Determinantal random subgraphs
Adrien Kassel, Thierry Lévy
We define two families of determinantal random spanning subgraphs of a finite connected graph, one supported by acyclic spanning subgraphs (spanning forests) with fixed number of c…
On the mean projection theorem for determinantal point processes
Adrien Kassel, Thierry Lévy
In this short note, we extend to the continuous case a mean projection theorem for discrete determinantal point processes associated with a finite range projection, thus strengthen…
Graph coverings and twisted operators
David Cimasoni, Adrien Kassel
Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these oper…
Determinantal probability measures on Grassmannians
Adrien Kassel, Thierry Lévy
We introduce and study a class of determinantal probability measures generalising the class of discrete determinantal point processes. These measures live on the Grassmannian of a…
A colourful path to matrix-tree theorems
Adrien Kassel, Thierry Lévy
In this short note, we revisit Zeilberger's proof of the classical matrix-tree theorem and give a unified concise proof of variants of this theorem, some known and some new.
Covariant Symanzik identities
Adrien Kassel, Thierry Lévy
Classical isomorphism theorems due to Dynkin, Eisenbaum, Le Jan, and Sznitman establish equalities between the correlation functions or distributions of occupation times of random…
Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for
Ewain Gwynne, Adrien Kassel, Jason Miller +1
We introduce a two-parameter family of probability measures on spanning trees of a planar map. One of the parameters controls the activity of the spanning tree and the other is a m…
Active spanning trees and Schramm-Loewner evolution
Adrien Kassel, David B. Wilson
We consider the Peano curve separating a spanning tree from its dual spanning tree on an embedded planar graph, where the tree and dual tree are weighted by to the number of ac…
Revisiting the combinatorics of the 2D Ising model
Dmitry Chelkak, David Cimasoni, Adrien Kassel
We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density…
The singularity probability of random diagonally-dominant Hermitian matrices
Adrien Kassel
In this note we describe the singular locus of diagonally-dominant Hermitian matrices with nonnegative diagonal entries over the reals, the complex numbers, and the quaternions. Th…
The looping rate and sandpile density of planar graphs
Adrien Kassel, David B. Wilson
We give a simple formula for the looping rate of loop-erased random walk on a finite planar graph. The looping rate is closely related to the expected amount of sand in a recurrent…
Transfer current and pattern fields in spanning trees
Adrien Kassel, Wei Wu
When a simply connected domain () is approximated in a "good" way by embedded connected weighted graphs, we prove that the transfer current matrix…
Random curves on surfaces induced from the Laplacian determinant
Adrien Kassel, Richard Kenyon
We define natural probability measures on cycle-rooted spanning forests (CRSFs) on graphs embedded on a surface with a Riemannian metric. These measures arise from the Laplacian de…
Random two-component spanning forests
Adrien Kassel, Richard Kenyon, Wei Wu
We study random two-component spanning forests (SFs) of finite graphs, giving formulas for the first and second moments of the sizes of the components, vertex-inclusion probabil…