Related papers: Propagation through trapped sets and semiclassical…
For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the…
The semiclassical approximation to the coherent state propagator requires complex classical trajectories in order to satisfy the associated boundary conditions, but finding these trajectories in practice is a difficult task that may…
We revisit previously developed analytic models for defect evolution and adapt them appropriately for the study of semilocal string networks. We thus confirm the expectation (based on numerical simulations) that linear scaling evolution is…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
We use a version of the Trotter-Kato approximation theorem for strongly continuous semigroups in order to study flows on growing networks. For that reason we use the abstract notion of direct limits in the sense of category theory.
A variation of Rosenstock's trapping model in which $N$ independent random walkers are all initially placed upon a site of a one-dimensional lattice in the presence of a {\em one-sided} random distribution (with probability $c$) of…
Recent years have witnessed a rise in real-world data captured with rich structural information that can be conveniently depicted by multi-relational graphs. While inference of continuous node features across a simple graph is rather…
We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target supported on finitely many points. This semi-discrete regime is the theoretical setting behind the use of Flow Matching for…
We develop a second-microlocal calculus of pseudodifferential operators in the semiclassical setting. These operators test for Lagrangian regularity of semiclassical families of distributions on a manifold $X$ with respect to a Lagrangian…
The study of wave propagation outside bounded obstacles uncovers the existence of resonances for the Laplace operator, which are complex-valued generalized eigenvalues, relevant to estimate the long time asymptotics of the wave. In order to…
Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under…
We describe the use of array expressions as constraints, which represents a consequent generalisation of the "element" constraint. Constraint propagation for array constraints is studied theoretically, and for a set of domain reduction…
Complex-valued semiclassical methods hold out the promise of treating classically allowed and classically forbidden processes on the same footing. In addition, they provide a natural way to describe optical excitation with complex fields…
In this article we study the propagation of Wigner measures linked to solutions of the Schr{\"o}dinger equation with potentials presenting conical singularities and show that they are transported by two different Hamiltonian flows, one over…
We study the resolvent norm of a certain class of closed linear operators on a Hilbert space, including unbounded operators with compact resolvent. It is shown that for any point in the resolvent set there exist directions in which the norm…
We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
This paper presents a novel pairwise constraint propagation approach by decomposing the challenging constraint propagation problem into a set of independent semi-supervised learning subproblems which can be solved in quadratic time using…
We study the high frequency limit for a non-dissipative Helmholtz equation. We first prove the absence of eigenvalue on the upper half-plane and close to an energy which satisfies a weak damping assumption on trapped trajectories. Then we…
We consider Schr\"odinger equations with variable coefficients, and it is supposed to be a long-range type perturbation of the flat Laplacian on $R^n$. We characterize the wave front set of solutions to Schr\"odinger equations in terms of…