45 citations · 173 across the 15 of their papers we have counts for
11 papers · 1 filter
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…
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…
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…
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…
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…