Random walks on groups

• Randomly Growing Braid on Three Strands and the Manta Ray (with F. Mathéus). Ann. Appl. Probab., 2007, Vol. 17, No. 2, 502­536. Abstract.ps, Paper.pdf. A version with an Appendix containing detailed computations is available on arXiv:math.PR/0512391.

• Random Walks on Groups and Monoids with a Markovian Harmonic Measure. (This is an updated and shortened version of the Research Report LIAFA 2004-005, Univ. Paris 7, 2004.) Electron. J. Probab., Vol. 10, p. 1417-1441, 2005. Abstract.ps, Article at Electron. J. Probab.

• Random walks on free products of cyclic groups (with F. Mathéus). (This is an updated and shortened version of the Research Report LIAFA 2004-006, Univ. Paris 7, 2004.) J. London Math. Soc., Vol. 75, n. 1, p. 47 -- 66, 2007. Abstract.ps, Paper.ps.gz. This article has an Appendix containing the bulk of the computations and available on arXiv:math.PR/0509208.

• An extended abstract announcing (without proofs) the results of the two above papers (with F. Mathéus). In Mathematics and computer science. III. Algorithms, trees, combinatorics and probabilities, p. 445-460, Trends in Mathematics, Birkhauser Verlag, 2004. Paper.ps.gz

Combinatorial (semi)group theory

• Computing the average height in trace monoids (with D. Krob and I. Michos). Discrete Mathematics. Vol. 273, p. 131-162, 2003. An abridged version appears in STACS 2002, Antibes-Juan les Pins, LNCS 2285, p.477-488, Springer. Abstract.ps, Paper.ps.gz.

• Mobius inversion formula for the trace group (with A. Bouillard). C. R. Acad. Sci. Paris, Ser. I, Vol. 339, n. 12, p. 899-904, 2004. Paper.ps.gz. A long version appeared as DLT'03 , LNCS 2710, p. 159-170, Springer. Abstract.ps, Paper.ps.gz.

• Growth series for Artin groups of dihedral type (with F. Mathéus). Internat. J. Algebra Comput., Vol. 16, No. 6, p. 1087-1107, 2006. Abstract.ps, Paper.ps.gz.

• Zero-automaticity for groups and monoids. (This is a rewritten version of Sections 3 and 5.1 of the Research Report LIAFA 2004-005, Univ. Paris 7, 2004.) Paper.ps.gz.

Discrete Event Dynamical Systems

Queueing networks

• Stationary Ergodic Jackson Networks: Results and Counter-Examples (with F. Baccelli and S. Foss). Stochastic networks, Oxford Univ. Press, p.281-307, 1996. Abstract.ps, Paper.ps.gz

• Asymptotic Results on Infinite Tandem Queueing Networks (with F. Baccelli and A. Borovkov). Probability Theory and Related Fields. Vol. 118, n. 3, p. 365-405, 2000. Abstract.ps, Paper.ps.gz

• On the Existence of Fixed Points for the ./GI/1 Queue (with B. Prabhakar). Annals of Probability. Vol. 31, n. 4, p. 2216-2236, 2003. Abstract.ps, Paper.ps.gz. LIAFA 99 Internal Report version: Paper.ps.gz.

• Services within a Busy Period of an M/M/1 Queue and Dyck Paths (with M. Draief). Queueing Systems, Vol. 49, p. 73-84, 2005. Paper.ps.gz

• Queues, Stores, and Tableaux (with M. Draief and N. O'Connell). J. Appl. Probab., Vol. 42, n. 4, p. 1145-1167, 2005. A short version without proofs appears in DMTCS, Discrete Random Walks 2003, n. 1893, 2003. Paper.ps.gz

• Zero-Automatic Queues and Product Form (with T.-H. Dao-Thi). Adv. Appl. Probab., Vol. 39, n. 2, p. 429-461, 2007. A short version appears in LNCS 3670, p. 64-78, Springer-Verlag, 2005. Abstract.ps, Paper.ps.

• Zero-Automatic Networks (with T.-H. Dao-Thi). To appear in Discrete Event Dynamical Systems, 2007. A short version appears in Proceedings of Valuetools, Pisa, Italy, ACM, 2006. Abstract.ps, Paper.ps.

Petri nets

• Computations of Uniform Recurrence Equations Using Minimal Memory Size (with Bruno Gaujal and Alain Jean-Marie). SIAM J. on Computing, Vol. 30, n. 5, p. 1701-1738, 2000. Abstract.ps, Paper.ps.gz

• Minimization of circuit registers: retiming revisited (with Bruno Gaujal). To appear in Discrete Appl. Math., 2007. Paper.pdf.

• Blocking a transition in a Free Choice net and what it tells about its throughput (with B. Gaujal and S. Haar). J. Comput. Syst. Sci, Vol. 66, n. 3, p. 515-548, 2003. Abstract.ps, Paper.ps.gz

• Extremal throughputs in free-choice nets (with A. Bouillard and B. Gaujal). Discrete Event Dynamical Systems, Vol. 16, n. 3, p. 327-352, 2006. Abridged version (without proofs) in: G. Ciardo and P. Darondeau, editors, 26th International Conference On Application and Theory of Petri Nets, LNCS 3670. Springer-Verlag, 2005. Abstract.ps, Paper.ps.gz

Tetris models

• Task Resource Models and (max,+) Automata (with S. Gaubert) Idempotency, Publications of the Isaac Newton Institute, Cambridge University Press, p.133-144, 1998. Abstract.ps, Paper.ps.gz

• Modeling and Analysis of Timed Petri Nets using Heaps of Pieces (with S. Gaubert). IEEE Trans. Autom. Control, Vol. 44, n. 4, p. 683-697, 1999. Abstract.ps, ShortPaper.ps.gz LongPaper.ps.gz. An illustration of the results of the paper in the form of a Maple worksheet is available here.

• Asymptotic behavior in a heap model with two pieces (with L. Vuillon). Theoretical Computer Science. Vol. 270, p. 525-560, 2002. Abstract.ps, Paper.ps.gz

• Asymptotic Analysis of Heaps of Pieces and application to Timed Petri Nets (with S. Gaubert). Petri Nets and Performance Models (PNPM'99), P. Bucholz and M. Silva eds, p. 158-169, IEEE Computer Society, 1999. Abstract.txt, Paper.ps.gz (version without proofs)

• Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture (with T. Bousch). J. Amer. Math. Soc. Vol. 15, p. 77-111, 2002. Also Univ. Paris 11, Mathématiques, Research Report 00/34, 2000. Abstract.ps, Paper.ps.gz.

(Max,+) algebra and topical functions

• Graphical Approach of the Spectral Theory in the (max,+) Algebra. IEEE Trans. Autom. Control, Vol. 40, n. 10, p. 1783-1789, 1995. Abstract.ps, Paper.ps.gz

• Products of Irreducible Random Matrices in the (max,+) Algebra. Adv. Applied Probability, Vol. 29, n. 2, p. 444-477, juin 1997. Abstract.ps, Paper.ps.gz

• Ergodic Theory of Stochastic Operators and Discrete Event Networks (with F. Baccelli). Idempotency, Publications of the Isaac Newton Institute, Cambridge University Press, p.171-208, 1998. Abstract.ps, Paper.ps.gz

• Bilinear functions and trees over the (max,+) semiring (with S. Mantaci and V. Blondel). Proceedings Mathematical Foundations of Computer Science (MFCS'00), LNCS 1893, p. 549-558, Springer-Verlag, 2000. Abstract.ps, Paper.ps.gz (version without proofs)

• Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture (with T. Bousch). J. Amer. Math. Soc. Vol. 15, p. 77-111, 2002. Also Univ. Paris 11, Mathématiques, Research Report 00/34, 2000. Abstract.ps, Paper.ps.gz.

• Finite-range topical functions and uniformly topical functions (with T. Bousch). Dynamical Systems, Vol. 21, n.1, p. 73-114, 2006. English version: Summary.ps, Article.ps.gz. French version: Resume.ps, Papier.ps.gz.

• Deciding Unambiguity and Sequentiality from a Finitely Ambiguous Max-Plus Automaton (with I. Klimann, S. Lombardy, and C. Prieur). Theoretical Computer Science Vol. 327, Issue 3, p. 349-373, 2004. A short version appeared as DLT'03 , LNCS 2710, p. 373-385, Springer, 2003. Abstract.ps, Paper.ps.gz.

• Series which are both max-plus and min-plus rational are unambiguous (with S. Lombardy). Theoret. Inform. Appl., Vol. 40, n. 1, p. 1-14, 2006. Abstract.txt, Paper.ps.gz.

Introductive texts on (max,+) algebra and discrete event systems

• Modélisation à l'aide de systèmes (max,+) linéaires. In French. Abstract.ps, Paper.ps.gz

• Petri Nets, (Max,+) Algebra and Scheduling. In Support de cours, 26-ieme ecole de printemps d'informatique theorique, INRIA Editeur, p.329-357, 1998.Abstract.ps, Paper.ps.gz

Other

Concours d'entrée a l'École Normale Supérieure (Ulm, Lyon, Cachan). (Entrance examination at the École Normale Supérieure, in french).
• Épreuve écrite d'informatique, concours MP, session 1999. Sujet de l'épreuve (avec B. Durand) Sujet99.ps.gz. Corrigé de l'épreuve (avec B. Durand et Y. Verhoeven). RMS : Revue des mathématiques de l'enseignement supérieur, n. 6, p. 642-657, février 2000. Corrige99.ps.gz.

• Épreuve écrite d'informatique, concours MP, session 2000. Sujet de l'épreuve (avec J. Cassaigne et A. Darte) Sujet00.ps.gz. Corrigé de l'épreuve (avec J. Cassaigne). RMS : Revue des mathématiques de l'enseignement supérieur, n. 8, p. 858-876, avril 2001. Corrige00.ps.gz.

• Épreuve écrite de Mathématiques-Informatique, concours Info, session 2002. Sujet de l'épreuve (avec A. Darte) Sujet02.ps.gz. Corrigé de l'épreuve (avec A. Darte). RMS : Revue des mathématiques de l'enseignement supérieur, 2003. Corrige02.ps.gz.

• Épreuve écrite de Mathématiques-Informatique, concours Info, session 2003. Sujet de l'épreuve (avec J. Goubault-Larrecq) Sujet03.ps.gz. Corrigé de l'épreuve (avec J. Goubault-Larrecq). Corrige03.ps.gz.