arXiv subjects

Fanch Coudreuse

Publications and source records attributed to Fanch Coudreuse.

4 recordsLinked to original sources

arXiv2026

Probabilistic representation and limit theorems for particle numbers of quasi-free states

We study the particle number distribution of locally interacting bosonic quasi- free states, which arise in various areas of mathematical physics. We show that the particle number decomposes into an infinite sum of independent geometrically distributed random variables, confirming predictions from the physics literature. This representation yields exponential tail bounds for the particle number, a law of small numbers together with a large deviation principle at logarithmic speed when the lattice spacing diverges, and a central limit theorem when it vanishes. As an application, we obtain a detailed description of the statistics of the quantum depletion in Bose--Einstein condensates, with the constants explicit in terms of the scattering length of the interaction potential.

math-ph↗

arXiv2026

An Aronson-B\'enilan / Li-Yau estimate in the JKO scheme in small dimension

We derive an Aronson-B\'enilan / Li-Yau estimate in the JKO scheme associated to the porous-medium, heat, and fast-diffusion equations, in dimensions $1$ and $2$, and on simple domains (cubes, quarter-space, half-spaces, whole space, and the torus). Our method is based on a maximum principle for the determinant of the Hessian of Brenier potentials, iterated as a one-step improvement along the scheme. As a consequence, we obtain local $L^\infty$ bounds on the density, uniform in the time step, consistent with the continuous-time result. As a byproduct, we rigorously derive the optimality conditions in the fast-diffusion case, filling a gap in the literature.

math.AP↗

arXiv2026

Generalized Logarithmic Sobolev Inequality by the JKO Scheme

Using a discrete Bakry-{\'E}mery method based on the JKO scheme, relying on the dissipation of entropy and Fisher information along a discrete flow, we establish new generalized logarithmic Sobolev inequality for log-concave measures of the form $e^{-V}$ under strict convexity assumptions on $V$ . We then show how this method recovers some well-known inequalities. This approach can be viewed as interpolating between the Bakry-{\'E}mery method and optimal transport techniques based on geodesic convexity.

math.AP↗

arXiv2025

Li-Yau-Hamilton Inequality on the JKO Scheme for the Granular-Medium Equation

We establish a version of the Li--Yau--Hamilton inequality for the Granular-Medium equation on the torus, both at the PDE level and for its time-discrete approximation given by the JKO scheme. We then apply this estimate to derive further quantitative results for the continuous and discrete JKO flows, including Lipschitz and $L^\infty$ bounds, as well as a quantitative Harnack inequality. Finally, we use the regularity provided by this estimate to show that the JKO scheme for the Fokker--Planck equation converges in $L^2_{\mathrm{loc}}((0,+\infty); H^2(\mathbb{T}^d))$.

math.AP↗