• Home
• Research
• Publications
• Mathematical Pictures
• Teaching
• Linux
• Annals Cachan 3A

Publications

• Gibbsian fields associated to exponentially decreasing
  Annales de l'Institut Henri Poincaré  1999, vol 35 n°3, pages 387-415. Mathscinet Abstract
• Asymptotic behaviour of Gaussian processes with integral representation
  Stochastic Processes and their Applications 2000, vol 89 n°2, pages 287-303. Mathscinet Abstract
• Infinite dimensional dynamics associated to quadratic Hamiltonians
  Markov Processes and Related Fields 2000, vol 6 n° 2, pages 205-237. Mathscinet Abstract
• Limit theorems for the painting of graphs by clusters
  European Series in Applied and Industrial Mathematics - Probability and Statistics (ESAIM-PS) 2001, vol 5, pages 105-118. Mathscinet Abstract
• Harmonic oscillators on an Hilbert space: a Gibbsian approach
  Potential Analysis 2002, vol 17 n° 1, pages 65-88. Mathscinet Abstract
• Percolation transition for some excursion sets
  Electronic Journal of Probability 2004, vol 9 paper n° 10, pages 255-292. Mathscinet
  We consider a random field \((X_n)_{n\in\mathbb{Z}^d}\) and investigate when the set \(A_h=\{k\in\mathbb{Z}^d; \vert X_k\vert \ge h\}\) has infinite clusters. The main problem is to decide whether the critical level \(h_c=\sup\{h\in\mathbb{R} ;P(A_h\text{ has an infinite cluster})>0\}\) is neither \(0\) nor \(+\infty\). Thus, we say that a percolation transition occurs. In a first time, we show that weakly dependent Gaussian fields satisfy to a well-known criterion implying the percolation transition. Then, we introduce a concept of percolation along reasonable paths and therefore prove a phenomenon of percolation transition for reasonable paths even for strongly dependent Gaussian fields. This allows to obtain some results of percolation transition for oriented percolation. Finally, we study some Gibbs states associated to a perturbation of a ferromagnetic quadratic interaction. At first, we show that a transition percolation occurs for superstable potentials. Next, we go to the the critical case and show that a transition percolation occurs for directed percolation when \(d\ge 4\). We also note that the assumption of ferromagnetism can be relaxed when we deal with Gaussian Gibbs measures, i.e. when there is no perturbation of the quadratic interaction.
• Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster
  joint work with Régine Marchand
  European Series in Applied and Industrial Mathematics - Probability and Statistics (ESAIM-PS) 2004, vol 8, pages 169-199. Mathscinet Abstract
• Coexistence in two-type first-passage percolation models
  joint work with Régine Marchand
  Annals of Applied Probability 2005, Vol. 15, No. 1A, pages 298-330. Mathscinet Abstract
• Central Limit Theorems for the Potts model
  Mathematical Physics Electronic Journal 2005, Vol. 11, paper n° 4. (27p) Mathscinet Abstract
• Competition between growths governed by Bernoulli Percolation
  joint work with Régine Marchand
  Markov Processes and Related Fields 2006, vol 12 n° 4, pages 695-734. Mathscinet Abstract
• Large deviations for the chemical distance in supercritical Bernoulli percolation
  joint work with Régine Marchand
  Annals of Probability 2007, vol 35 n° 3, pages 833-866. Mathscinet Abstract
• First-passage competition with different speeds: positive density for both species is impossible
  joint work with Régine Marchand
  Electronic Journal of Probability 2008, vol 13 paper n° 70, pages 2118-2159. Mathscinet Abstract
• Capacitive flows on a 2D random net
  Annals of Applied Probability 2009, vol 19 n° 2, pages 641-660. Mathscinet Abstract
• Moderate deviations for the chemical distance in Bernoulli percolation
  joint work with Régine Marchand
  Alea 2010, vol 7, pages 171-191. Mathscinet Abstract
• Asymptotic shape for the contact process in random environment
  joint work with Régine Marchand
  Annals of Applied Probability 2012, vol 22 n° 4, pages 1362-1410 Mathscinet Abstract
• Bacterial persistence: a winning strategy?
  joint work with Régine Marchand Rinaldo Schinazi
  Markov Processes and Related Fields 2012, vol 18 n° 4, pages 639-650 Mathscinet Abstract
• The critical branching random walk in a random environment dies out
  joint work with Régine Marchand
  Electronic Communications in Probability 2013, vol 18 article n° 9, pages 1-15. Mathscinet Abstract
• Large deviations for the contact process in random environment
  joint work with Régine Marchand
  Annals of Probability 2014, vol 42 n° 4, pages 1438-1479. Mathscinet Abstract
• Growth of a population of bacteria in a dynamical hostile environment
  joint work with Régine Marchand
  Advances in Applied Probability 2014, vol 46 n°3, pages 661-686. Mathscinet Abstract
• Les lois Zéta pour l'arithmétique
  Quadrature 2015, Avril-mai-juin, n°96, pages 10-18 Mathscinet Abstract
• Continuity of the asymptotic shape of the supercritical contact process
  joint work with Régine Marchand Marie Théret
  Electronic Communications in Probability 2015, vol 20 article n° 92, pages 1-11. Abstract
• The number of open paths in oriented percolation
  joint work with Régine Marchand Jean-Baptiste Gouéré
  Annals of Probability 2017, vol 45 n° 6A, pages 4071-4100. Mathscinet Abstract
• Continuity of the time and isoperimetric constants in supercritical percolation
  joint work with Régine Marchand Eviatar Procaccia Marie Théret
  Electronic Journal of Probability 2017, vol 22 article n° 78, 35 pp Mathscinet Abstract
• Does Eulerian percolation on \(\mathbb{Z}^2\) percolate?
  joint work with Régine Marchand Irene Marcovici
  Alea 2018, vol 15 article 13, pages 279-294. Abstract
• Percolation and first-passage percolation on oriented graphs
  joint work with Régine Marchand
  Electronic Communications in Probability 2021, vol 26, paper no. 50, pages 1-14 Abstract
• A Central Limit Theorem for the number of descents and some urn models
  Markov Processes and Related Fields 2021, vol 27, no 5, pages 789-801 Abstract
• A simple master Theorem for discrete divide and conquer recurrences
  North-Western European Journal of Mathematics 2022, vol 8, pages 91-101 Abstract

Preprints

• Growth of a population of bacteria in a dynamical hostile environment
  joint work with Régine Marchand
  preprint ArXiV: q-bio & math.PR/1010.4618 HAL: 00528471
• A simple master Theorem for discrete divide and conquer recurrences
  preprint ArXiV: math.CA/1902.10600 HAL: hal-2049382
• Probabilistic proof for non-survival at criticality: the Galton-Watson process and more
  preprint ArXiv: math.PR/2202.00256 HAL: hal-03546828

Most of my recent preprints are also available on ArXiv.

If you want to read an article which is not on-line, send me an e-mail.