Main Research Themes : Interacting particle systems and Hydrodynamic limits

- Interacting systems.
- Short and long range interactions.
- Model studies.

PhD Studies at Université Aix-Marseille I (France), I had the chance to visit, learn and spend time at
IME-USP São Paulo (Brazil), IMPA Rio de Janeiro (Brazil), Math. Dept. Rochester university (USA),
UnB. Brasilia (Brazil), SUNY College at New Paltz (USA), IMECC-Unicamp Campinas (Brazil), Univ. Méditéranée (France), Lab.R. Salem Univ. Rouen (France),  Universitat GH Essen (Germany), IMA-EPFL Lausanne (Switzerland), IHP Paris (France), Math. Dept. at UCCS Colorado Springs (USA).

Academic Genealogy : http://www.genealogy.ams.org/index.php
(E. Andjel, T. Liggett, S. Karlin, S. Bochner, E. Schmidt, D. Hilbert,...)

Main collaborators:
E. Andjel (U. Marseille I) ;
C. Bahadoran (U. Clermont-Ferrand II) ; P.A. Ferrari, (USP) ; M.V. Freire (USP)
A. Galves (USP); C. Landim (CNRS, Rouen); F. Machado (USP); T. Mountford (EPF Lausanne) ;
K. Ravishankar (SUNY);
E. Saada (CNRS, Paris V); R. Schinazi (UCCS).

Key words and phrase:
Stochastic processes, stochastic models, interacting particle systems, hydrodynamic limit, ergodic theorems, non Feller process.


Partners & projects:
- Phase transitions and fluctuation phenomena for random dynamics in spatially extended systems, European Science Foundation.
- Partner ANR
Blan 2006-2009 Modèles Aléatoires pour l'Evolution du Vivant. Acronyme : MAEV
- Partner ANR Blan 2007-2010 Limites Hydrodynamiques et Mécanique Statistique Hors Equilibre. Acronyme : LHMSHE
- Partner ANR Blan 07-2184264 2010-2013 Systèmes Hors Equilibre de Particules en Interaction. Acronyme : Acronyme : SHEPI
- "Systèmes de particules" Projet IXXI - Institut des Systèmes Complexes Rhone Alpes, 2007-2009.
- Partner PICS 5470, 2010-2012 Systèmes à une infinité de particules en interaction et applications en physique et biologie
- Since 2012 : Member of the Scientific Commitee of the LICIA Lab : http://licia-lab.org/

Research team
- Member of the BCM team directed by O. François in the TIMC Lab directed by P. Cinquin

List of Invited Talks
June 2011, 35th Conference on Stochastic Processes and their Application - Oxaca , Mexico :
    Species survival time in an evolution model. PDF
May 23rd 2011 Palestra no DAS, UFSC Florianopolis, Brasil
November 16th 2010 Séminaire à l'IXXI ENS Lyon, France
September 3rd 2010 Journées MAS - Bordeaux, France
December 10th 2009 ANR MAEV - UPMC Paris
August 20th 2009 NUMEC - IME USP Sao Paulo, Brasil
January 22th 2009 Dept. of Mathematics - Colorado Springs, USA:
   Almost sure scaling limit for monotone particle systems on $\Z$. PDF

Publications
 
[16] Bahadoran, C., Guiol, H.,  Ravishankar, K and Saada E. (2012)
Euler hydrodynamics for attractive particle systems in random environment.
To appear in Annales de l'Institut Henri Poincaré - Probablités et Statistiques.
arXiv:1201.2160

[15] Guiol, H., Machado, F.P. and  Schinazi, R.B. (2013) 
On a link between a species survival time in an evolution model and the Bessel distributions.
Braz. J. Probab. Stat. Vol 27, No. 2, 201--209.
or arXiv preprint.

[14] Guiol, H., Machado, F.P. and  Schinazi, R.B. (2011)
A stochastic model of evolution.
Markov Processes Relat. Fields
17, 253--258.
Available from arXiv.
MR2856242

[13] Bahadoran, C., Guiol, H.,  Ravishankar, K. and Saada E. (2010).
Strong hydrodynamic limit for attractive particle systems on Z. 
Electronic Journal of Probability. Vol 15, Paper no.1, 1--43.
MR2578381 (2011e:60218)

[12]  Bahadoran, C., Guiol, H.,  Ravishankar, K and Saada E. (2006).
Euler Hydrodynamics of one-dimensional attractive particle systems.
Ann. Probab.
Vol 34, No. 4, 1339--1369.
Available from  ArXiv
MR2257649

[11]  Guiol, H., Mountford, T. (2006)
Questions for second class particles in exclusion processes.
 Markov Processes and Related Fields. Vol. 12, No. 3, 301--308
PDF
MR2249633

[10] Andjel, E.D., Guiol, H. (2005)
Long range exclusion processes, generator and invariant measures.
 Ann. Probab. Vol 33, No. 6, 2314--2354.
Available from  ArXiv
MR2184098

[9]  Mountford, T., Guiol, H. (2005)
The motion of a second class particle for the TASEP starting from a decreasing shock profile.
 Ann. Appl. Probab. Vol 15, No. 2, 1227--1259.
Available from  ArXiv
MR2134103

[8] Guiol, H. (2004)
About the long range exclusion process.
Proceedings of the ``Gibbs vs Non Gibbs" Conference, EURANDOM, 
Markov Processes and Related Fields
. Vol 10, 457--476.
PDF (preprint version)
MR2097867

[7] Guiol, H., Ravishankar, K. and Saada, E. (2003)
Microscopic structure of a decreasing shock for the asymmetric k-step exclusion process.
 Electron. Comm. Probab. Vol 8, Paper no. 19, 170--178.
MR2042756

[6] Freire, M.V., Guiol, H., Ravishankar, K. and Saada, E. (2002)
Microscopic structure of the $k$-step exclusion process.
Fifth   Brazilian School in Probability (Ubatuba, 2001).
Bull. Braz. Math. Soc. (N.S.) Vol 33, No. 3, 319--339.
PDF (preprint version)
MR1 978 831

[5] Bahadoran, C., Guiol, H.,  Ravishankar, K. and Saada, E. (2002)
A constructive approach to Euler hydrodynamics for attractive processes. Application to
k-step exclusion.
Stochastic Processes and their Applications.
Vol 99, No. 1, 1--30.
PDF (preprint version)
MathRev 2003h:60140

[4] Andjel, E.D.,  Ferrari, P.A., Guiol, H. and Landim C. (2000).
Convergence to the maximal invariant measure in zero range process with random rates.
Stochastic Processes and their Applications. Vol 90, No. 1, 67--81.
PDF (preprint version)
MathRev 2001h:60172

[3] Guiol, H. (1999)
Some properties of k-step exclusion processes.
 Journal of Statistical Physics. Vol 94, No 3/4, 495--511.
PDF (preprint version)
MathRev 2000e:60181

[2] Galves, A. and Guiol, H. (1997)
Relaxation time to equilibrium of the one-dimensional symmetric zero range process with constant rate.
Markov Processes
and Related Fields. Vol  3, No 3, 323--332 .
PDF (preprint version)
MathRev 98m:60151

[1] Guiol, H. (1997)
Un résultat pour le Processus d'Exclusion à Longue Portée.
Annales de l'Institut Henri Poincaré: B, Probabilités et Statistiques
. Vol 33, No 4, 387--405.
PDF (preprint version)
MathRev 98m:60152

Books

[1] with M. Gneri et A. Pinheiro. Probabilidade I. (in Portuguese) .
[2]  with M. Gneri et A. Pinheiro. Probabilidade II. (in Portuguese).
 

Technical Report

[1] Guiol, H. (1997) A note on a Burton-Keane's theorem. Technical Report RT-MAE 9707 IME-USP.

[2] With A. Koukkous (2000) Large deviations in random media of zero mean asymmetric zero range processes.
23 pages, Relatorio de Pesquisa RP 16/00 IMECC-UNICAMP. PDF (preprint version)
 
Direction of Research Initiation Reports

(2011)
- Systèmes de particules en interaction. Thomas Guillet (Lien EnsiWiki)
(2010)
-
Utilisation des arbres binomiaux pour le pricing des options américaines. Anne-Victoire Auriault (Lien EnsiWiki)
(2009)
- Modèles stochastiques de propagation d'épidémies. Adolfo Olguín-Gutiérrez (Lien EnsiWiki)

Direction of Speciality's Projects
(2011)
-
Arbitrage et Modélisation de paris sportifs. (co-encadrant M. Echemin) R. Comtet, P.A. Lacagne, A. Truc-Vallet
-Logiciel de détection d'un délit d'initié. (co-encadrant M. Echemin)  N.A. Drouet, A. Jeribi, M. Lassoued, D. Quesnel
(2010)
- Détection d'un délit d'initié. (co-encadrant M. Echemin) P. Blaque, A. Lyson et X. Houang
- Même titre : S. Bousquet, N. Lecluse, C. Lemaire et N. Mesme
- Détection d'une crise Financière (co-encadrant M. Echemin)  A. Braud et R. Schaefer
- Même titre : B. Mayeur et K. Lourd.
(2009)
-Arbitrage et Modélisation de paris sportifs. Y. Belayachi et A.A. El Ghazi
-Même titre. M. Boussab et D. Masaoudi.
(2008)
-Modèles aléatoires pour la propagation d'épidémie. E. Bahraoui et A. Zahiri
-Modélisation d'un délit d'initié (co-encadrant: T. Burger). R. Bompis, H. Merat, G. Personnettaz et J. Rolland
(2007)
-Modèle de propagation d'épidémie avec contrainte spatiales. L. Gattepaille et F. Jay
-Option d'achat et de vente à partir des résultats du championnat de France de football. A. Guerin et C. Mignardot
-Même titre. R. Fellous et T. Cohades
(2006)
-Modélisation d'épidémie. B. Chomel et T. Roux
-Etude de la propagation d'une épidémie. D. Sportouch et L. Toni
(2005)
-Processus de Lévy E. Giraud et B. Jacob
-Etude et simulation des processus de Lévy H.D. Taban et C. Dridi
-Modèles de contrôle de trafic routier. B. Angéniol et A. Lefèvre
-Simulation du traffic routier. L. Sourdin et M. Vignaud

Former Students

Abdellatif Koukkous, present position : Assistant Professor at Université Ibn Zohr d'Agadir, Maroc
Former post-doc felow at IMECC-UNICAMP Brazil sep 1999/aug 2000
Support : FAPESP

Marcelo Ventura Freire, present position : Professor Doutor, Universidade de São Paulo, Brésil
Mestrado defended on 12/01/2001 :  Fenômenos de Localisaçao em Passeio Aleatorio com potencial aleatorio.
Support : FAPESP

Last modified 28/09/2012.