Publications

PREPRINTS:

PUBLICATIONS:

  1. with Luca Avena, Alexandre Gaudillière, Clothilde Mélot. Approximate and exact solutions of intertwining equations through random spanning forests. arXiv:1702.05992 [math.PR]. In and out of equilibrium. 3. Celebrating Vladas Sidoravicius, 27–69, Progr. Probab., 77, Birkhäuser/Springer, Cham, [2021],
  2. with Luca Avena, Alexandre Gaudillière, Clothilde Mélot. Intertwining wavelets or Multiresolution analysis on graphs through random forests . arXiv:1707.04616 [cs.IT,math.PR]. Appl. Comput. Harmon. Anal. 48 (2020), no. 3, 949–992.
    This paper constructs wavelets on graphs, and the associated multiresolution analysis for signal on graphs. The corresponding software developed by Dominique Benielli on Scython, is freely available here . Please use it!!
  3. with Luca Avena, Alexandre Gaudillière, Clothilde Mélot. Random forests and Network analysis. J. Stat. Phys. 173 (2018), no. 3-4, 985–1027. https://doi.org/10.1007/s10955-018-2124-8 [openaccess]
  4. with Nathalie Grafféo, Aurélien Bellot, Roch Giorgi. A log-rank type test to compare net survival distributions. Biometrics. Volume 72, Issue 3, 760-769 (September 2016).
  5. with Nadine Guillotin-Plantard, Frédérique Watbled. Persistence exponent for random processes in Brownian scenery. ALEA, Lat Am. J. Probab. Math. Stat. 13, 79-94 (2016).
  6. with Clément Laurent, Clothilde Mélot. Exponential moments of self- intersection local times of stable random walks in subcritical dimensions. J. Lond. Math. Soc. (2) 89 (2014), no 3, 876-902.
  7. with Nadine Guillotin-Plantard, Françoise Pène, Bruno Schapira. On the local time of random processes in random scenery. Annals of Probability (2014), Vol. 42, No 6, 2417-2453. ArXiv version.
  8. with Nadine Guillotin-Plantard, Françoise Pène, Bruno Schapira. On the one- sided exit problem for stable processes in random scenery. Electronic Communications in Probability (2013), Vol. 18, No 33, 1-7.
  9. with Nadine Guillotin-Plantard, Françoise Pène. Limit theorems for one and two-dimensionam random walk in random scenery. Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (2013), Vol. 49, No 2, 506-528.
  10. with Onur Gün, Grégory Maillard. Parabolic Anderson Model with a finite number of catalysts. In : Probability and Complex Physical Systems, Springer Proceedings in Mathematics 11, pp. 91-117, 2012.
  11. with Nadine Guillotin-Plantard, Françoise Pène, Bruno Schapira. A local limit theorem for random walks in random scenery and on randomly oriented lattices. Annals of Probability (2011), Vol. 39, No 6, 2079-2118.
  12. Large deviations for intersection local times in critical dimension. Ann. Probab. 38 (2010), no. 2, 927-953.
  13. with Amine Asselah. Random walk in random scenery and self-intersection local times in dimensions d ≥ 5. Probab. Theory Related Fields 138 (2007), no. 1-2, 1-32.
  14. with Amine Asselah. A note on Random Walk in Random Scenery. Ann. Inst. H. Poincaré Probab. Statist. 43 (2007), no. 2, 163-173.
  15. Moderate deviations for diffusions in a random Gaussian shear flow drift. Ann. Inst. H. Poincaré Probab. Statist. 40 (2004), no. 3, 337-366.
  16. with Amine Asselah. Large deviations for Brownian motion in a random scenery. Probab. Theory Related Fields 126 (2003), no.4, 497-527.
    In this paper, we stated a quenched Large Deviations Principle for the Brownian motion in random scenery without checking the positivity of the corresponding rate function. We are really sorry for this! This note is a proof of the positivity of the rate function.
  17. with Amine Asselah. Existence of quasi-stationary measures for asymmetric attrac- tive particle systems on Zd. Ann. Appl. Probab. 13 (2003), no. 4, 1569-1590.
  18. with Amine Asselah. Quenched large deviations for diffusions in a random Gaussian shear flow drift. Stochastic Process. Appl. 103 (2003), no. 1, 1-29.
  19. Homogenization of random semi-linear PDEs. Probab. Theory Related Fields 121 (2001), no. 4, 492-524
  20. with Frédéric Pradeilles. Annealed Large deviations for diffusions in a random shear flow drift. Stochastic Process. Appl. 94 (2001), no. 2, 171-197.
  21. with Gérard Ben Arous. A probabilistic approach to semi-classical approximations. Journal of Functional Analysis, vol. 137, no 1, 1996, p. 243-280.
  22. with Gérard Ben Arous. Flow decomposition and large deviations. J. Funct. Anal. 140, no 1, 1996, p. 23-67.
  23. with Jessica Gaines. The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations. Annales de l'Institut Henri Poincaré, série Probabilités et Statistiques, vol. 32, no 2, 1996, p. 231-250.
  24. with Jessica Gaines. An efficient approximation method for stochastic differential equations by means of the exponential Lie series. Proceedings du congrès Probabilités Numériques. Mathematics and Computers in Simulation 38, 1995, p.13-19, Elsevier Eds.
  25. Asymptotic expansions of stochastic flows. Probability Theory and Related Fields 96, pp 225-239 (1993).

SOFTWARE:

  1. IntertwiningWavelet toolbox: Pyramidal algorithms for wavelet decomposition on Graphs.

    The IntertwiningWavelet package is a Python Package for wavelet analysis on graphs. This toolbox is dedicated to a method called IntertwiningWavelet (IW) which provides a multiresolution analysis on non oriented graphs. It provides a wavelet basis on a graph and can analyse a bunch of signals defined on this graph. The method is fully described and analysed in this paper and a quicker description can be found in this one . The approach relies on probabilistic tools: a random spanning forest to downsample the set of vertices, and approximate solutions of Markov intertwining relation to provide a subgraph structure and a filterbank which is a basis of the set of functions. As a by-product, the method provides a graph coarse-graining procedure.
    The original iw Toolbox is developed in Python/Cython at LabEx Archimède, as a I2M project, by Dominique Benielli. Documentation is available on this public site.