20 citations · 32 across the 9 of their papers we have counts for
13 papers
Low-Temperature Large Deviations for the Two-Dimensional Wick-Ordered Cubic Wave Equation
Daniel Heydecker
We prove a trajectory large deviation principle, in the low-temperature limit, for the two-dimensional Wick-ordered defocusing cubic nonlinear wave equation, with initial data draw…
Pathological Large Deviations of the KMP Process in Dimension
Daniel Heydecker
We study dynamic large deviations for the Kipnis--Marchioro--Presutti process on the discrete torus . By recasting the candidate rate function in terms of a linear…
Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality
Benjamin Gess, Daniel Heydecker, Zhengyan Wu
The dynamical large deviations principle for the three-dimensional incompressible Landau-Lifschitz-Navier-Stokes equations is shown, in the joint scaling regime of vanishing noise…
The Porous Medium Equation: Large Deviations and Gradient Flow with Degenerate and Unbounded Diffusion
Benjamin Gess, Daniel Heydecker
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic parti…
Delving Into Deep Walkers: A Convergence Analysis of Random-Walk-Based Vertex Embeddings
Dominik Kloepfer, Angelica I. Aviles-Rivero, Daniel Heydecker
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph…
Large Deviations of Kac's Conservative Particle System and Energy Non-Conserving Solutions to the Boltzmann Equation: A Counterexample to the Predicted Rate Function
Daniel Heydecker
We consider the dynamic large deviation behaviour of Kac's collisional process for a range of initial conditions including equilibrium. We prove an upper bound with a rate function…
Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials
Nicolas Fournier, Daniel Heydecker
We establish the well-posedness and some quantitative stability of the spatially homogeneous Landau equation for hard potentials, using some specific Monge-Kantorovich cost, assumi…
Kac's Process with Hard Potentials and a Moderate Angular Singularity
Daniel Heydecker
We investigate Kac's many-particle stochastic model of gas dynamics in the case of hard potentials with a moderate angular singularity, and show that the noncutoff particle system…
Dynamic Spectral Residual Superpixels
Jianchao Zhang, Angelica I. Aviles-Rivero, Daniel Heydecker +3
We consider the problem of segmenting an image into superpixels in the context of -means clustering, in which we wish to decompose an image into local, homogeneous regions corre…
Bilinear Coagulation Equations
Daniel Heydecker, Robert I. A. Patterson
We consider coagulation equations of Smoluchowski or Flory type where the total merge rate has a bilinear form for a vector of conserved quantities , generalis…
Mirror, Mirror, on the Wall, Who's Got the Clearest Image of Them All? - A Tailored Approach to Single Image Reflection Removal
Daniel Heydecker, Georg Maierhofer, Angelica I. Aviles-Rivero +4
Removing reflection artefacts from a single image is a problem of both theoretical and practical interest, which still presents challenges because of the massively ill-posed nature…
Peekaboo - Where are the Objects? Structure Adjusting Superpixels
Georg Maierhofer, Daniel Heydecker, Angelica I. Aviles-Rivero +2
This paper addresses the search for a fast and meaningful image segmentation in the context of -means clustering. The proposed method builds on a widely-used local version of Ll…
Pathwise Convergence of the Hard Spheres Kac Process
Daniel Heydecker
We derive two estimates for the deviation of the -particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Partic…