Publications

2026

• Quantitative sensitivity analysis for Fokker-Planck equation with respect to the Wasserstein distance
  
  • Morange Martin
  , 2026. We analyze the sensitivity of solutions to the Fokker-Planck equation with respect to some unknown parameter. Our main result is to provide quantitative upper bounds for the $p$-Wasserstein distance $\mathcal{W}_p$ between two solutions with different parameters, for every $p \geq 2$. We are able to give two proofs of this result, the first relying on synchronous coupling between two solutions of an SDE, and another one that relies on the differentiation of Kantorovitch dual formulation of optimal transport. We also provide more specific bounds in the case of the overdamped Langevin process, for which we are able to compare convergence to the invariant measure and sensitivity to the parameter.
• Turing Instability for Nonlocal Heterogeneous Reaction-Diffusion Systems: A Computer-Assisted Proof Approach
  
  • Payan Maxime
  • Breden Maxime
  • Reisch Cordula
  • Tang Bao Quoc
  Journal of Dynamics and Differential Equations, Springer Verlag, 2026. This paper provides a computer-assisted proof for the Turing instability induced by heterogeneous nonlocality in reaction-diffusion systems. Due to the heterogeneity and nonlocality, the linear Fourier analysis gives rise to strongly coupled infinite differential systems. By introducing suitable changes of basis as well as the Gershgorin disks theorem for infinite matrices, we first show that all N -th Gershgorin disks lie completely on the left half-plane for sufficiently large N . For the remaining finitely many disks, a computer-assisted proof shows that if the intensity δ of the nonlocal term is large enough, there is precisely one eigenvalue with positive real part, which proves the Turing instability. Moreover, by a detailed study of this eigenvalue as a function of δ, we obtain a sharp threshold δ * which is the bifurcation point for Turing instability. (10.1007/s10884-026-10488-0)
  DOI : 10.1007/s10884-026-10488-0
• Separation rates for the detection of synchronization of interacting point processes in a mean field frame. Application to neuroscience.
  
  • Tchouanti Josué
  • Löcherbach Éva
  • Reynaud-Bouret Patricia
  • Tanré Etienne
  Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2026, 20 (1), pp.560--632. Permutation tests have been proposed by Albert et al. (2015) to detect dependence between point processes, modeling in particular spike trains, that is the time occurrences of action potentials emitted by neurons. Our present work focuses on exhibiting a criterion on the separation rate to ensure that the Type II errors of these tests are controlled non asymptotically. This criterion is then discussed in two major models in neuroscience: the jittering Poisson model and Hawkes processes having \(M\) components interacting in a mean field frame and evolving in stationary regime. For both models, we obtain a lower bound of the size \(n\) of the sample necessary to detect the dependency between two neurons. (10.1214/26-EJS2483)
  DOI : 10.1214/26-EJS2483