Publications

2025

P. Biane, Combinatorics of the quantum symmetric simple exclusion processes associahedra and free cumulants..
Ann. Henri Poincaré D 12 (2025), no.1, pp. 189-206

2024

M. Bauer, D. Bernard, P. Biane, L. Hruza, Bernoulli Variables, Classical Exclusion Processes and Free Probability.
Ann. Henri Poincaré 25 (2024), no.1, pp. 125-172

2021

P. Biane, Mating of discrete trees and walks in the quarter-plane
The Electronic Journal of Combinatorics, Volume 28, Issue 3 (2021), Article number P3.56

P. Biane, Nonlinear free Lévy--Khinchine formula and conformal mapping
Journal of Operator Theory, Volume 85, Issue 1, Winter 2021, pp. 79-99

2019

P. Biane, Laver tables and combinatorics
Séminaire Lotharingien de Combinatoire, B80c (2019), 24 pp.

P. Biane, M. Josuat-Vergès. Noncrossing partitions, Bruhat order and the cluster complex
Annales de l'Institut Fourier, Tome 69, no. 5, 2241-2289 (2019)

2018

P. Biane; Gog and Magog triangles
Computation and Combinatorics in Dynamics, Stochastics and Control The Abel Symposium, Rosendal, Norway, August 2016. Abel Symposia, Vol. 13, pp. 99--127 (2018).

2017

P. Biane, G. Chapuy. Laplacian matrices and spanning trees of tree graphs
Annales de la faculté des sciences de Toulouse Sér. 6, 26 no. 2, 235-261 (2017). arXiv

2016

P. Biane, M. Josuat-Vergès. Minimal factorizations of a cycle: a multivariate generating function
FPSAC 2016, DMTCS Proc. BC, 2016, 239-250 arXiv

P. Biane, H. Cheballah. Gog and GOGAm pentagons
Journal of Combinatorial Theory, Series A Volume 138, 133-154 (2016)

2015

P. Biane. Polynomials associated with finite Markov chains
Séminaire de Probabilités XLVII, 249-262, Lecture Notes in Mathematics, 2137, Springer, Berlin, 2015. arXiv

2014

P. Biane, P. Dehornoy. Dual Garside structure of braids and free cumulants of products
Séminaire Lotharingien de Combinatoire, B72b (2014), 15 pp.

P. Biane. Orthogonal Polynomials on the Unit Circle, q-Gamma weights, and Discrete Painlevé Equations
Moscow Mathematical Journal Volume 14, Issue 1, January-March 2014 pp. 1-27. arXiv

2013

P. Biane, H. Cheballah. Gog, Magog and Schützenberger II: left trapezoids.
FPSAC 2013, 349-360, Discrete Math. Theor. Comput. Sci. Proc., AS, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2013.

P. Biane, Y. Dabrowski. Concavification of free entropy
Advances in Mathematics 234 (2013), pp. 667-696 arXiv

2012

P. Biane, H. Cheballah. Gog and Magog Triangles, and the Schützenberger Involution
Séminaire Lotharingien de Combinatoire, B66d (2012), 20 pp.

P. Biane, L. Cantini, A. Sportiello. Doubly-refined enumeration of alternating sign matrices and determinants of 2-staircase Schur functions
Séminaire Lotharingien de Combinatoire, B65f (2012), 25 pp.

2011

P. Biane. Entrelacements de semi-groupes provenant de paires de Gelfand
ESAIM Probab. Stat. 15 (2011), In honor of Marc Yor, suppl., S2-S10.

P. Biane, G. Letac. The mean perimeter of some random plane convex sets generated by a Brownian motion
J. Theoret. Probab. 24 (2011), no. 2, 330-341. arXiv

2010

P. Biane. Itô's stochastic calculus and Heisenberg commutation relations
Stochastic Process. Appl. 120 (2010), no. 5, 698-720.

2009

P. Biane. Matrix valued Brownian motion and a paper by Pólya
Séminaire de probabilités XLII, 171-185, Lecture Notes in Math., 1979, Springer, Berlin, 2009. arXiv

P. Biane. Shabat polynomials and harmonic measure
Séminaire de probabilités XLII, 147-151, Lecture Notes in Math., 1979, Springer, Berlin, 2009.

P. Biane. From Pitman's theorem to crystals
Noncommutativity and singularities, 1-13, Adv. Stud. Pure Math., 55, Math. Soc. Japan, Tokyo, 2009.

P. Biane, P. Bougerol, N. O'Connell. Continuous crystal and Duistermaat-Heckman measure for Coxeter groups
Adv. Math. 221 (2009), no. 5, 1522-1583. arXiv

2008

P. Biane. Introduction to random walks on noncommutative spaces
Quantum potential theory, 61-116, Lecture Notes in Math., 1954, Springer, Berlin, 2008.

2006

P. Biane. Le théorème de Pitman, le groupe quantique SUq(2), et une question de P. A. Meyer
In memoriam Paul-André Meyer: Séminaire de Probabilités XXXIX, 6-75, Lecture Notes in Math., 1874, Springer, Berlin, 2006.

2005

P. Biane. On the formula of Goulden and Rattan for Kerov polynomials
Sém. Lothar. Combin. 55 (2005/07), Art. B55d, 5 pp.

P. Biane, P. Bougerol, N. O'Connell. Littelmann paths and Brownian paths
Duke Math. J. 130 (2005), no. 1, 127-167. arXiv

2004

J. Bertoin, P. Biane, M. Yor. Poissonian exponential functionals, q-series, q-integrals, and the moment problem for log-normal distributions
Seminar on Stochastic Analysis, Random Fields and Applications IV, 45-56, Progr. Probab., 58, Birkhäuser, Basel, 2004.

P. Biane. Nombre de factorisations d'un grand cycle
Sém. Lothar. Combin. 51 (2004/05), Art. B51a, 4 pp.

2003

P. Biane. Free probability for probabilists
Quantum probability communications, Vol. XI (Grenoble, 1998), 55-71, QP-PQ, XI, World Sci. Publ., River Edge, NJ, 2003, arXiv

P. Biane. Characters of symmetric groups and free cumulants
Asymptotic combinatorics with applications to mathematical physics (St. Petersburg, 2001), 185-200, Lecture Notes in Math., 1815, Springer, Berlin, 2003.

P. Biane. Logarithmic Sobolev inequalities, matrix models and free entropy
International Workshop on Operator Algebra and Operator Theory (Linfen, 2001). Acta Math. Sin. (Engl. Ser.) 19 (2003), no. 3, 497-506.

P. Biane. La fonction zêta de Riemann et les probabilités La fonction zêta,
165-193, Ed. éc. Polytech., Palaiseau, 2003

P. Biane, M. Capitaine, A. Guionnet. Large deviation bounds for matrix Brownian motion
Invent. Math. 152 (2003), no. 2, 433-459.

P. Biane, F. Goodman, A. Nica. Non-crossing cumulants of type B
Trans. Amer. Math. Soc. 355 (2003), no. 6, 2263-2303 arXiv

2002

P. Biane. Entropie libre et algèbres d'opérateurs
Séminaire Bourbaki, Vol. 2000/2001. Astérisque No. 282 (2002), Exp. No. 889, ix, 279-300.

P. Biane. Free probability and combinatorics
Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 765-774, Higher Ed. Press, Beijing, 2002.

P. Biane. Parking functions of types A and B
Electron. J. Combin. 9 (2002), no. 1, Note 7, 5 pp.

P. Biane. Combien de fois faut-il battre un jeu de cartes?
Gaz. Math. No. 91 (2002), 4-10.

P. Biane, E. Germain. Actions moyennables et fonctions harmoniques
C. R. Math. Acad. Sci. Paris 334 (2002), no. 5, 355-358.

2001

P. Biane. Free cumulants and representations of large symmetric groups
XIIIth International Congress on Mathematical Physics (London, 2000), 321-326, Int. Press, Boston, MA, 2001

P. Biane, D. Voiculescu. A free probability analogue of the Wasserstein metric on the trace-state space
Geom. Funct. Anal. 11 (2001), no. 6, 1125-1138. arXiv

P. Biane, F. Lehner Computation of some examples of Brown's spectral measure in free probability.
Colloq. Math. 90 (2001), no. 2, 181-211. arXiv

P. Biane, R. Speicher. Free diffusions, free entropy and free Fisher information
Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), no. 5, 581-606.

P. Biane, J. Pitman, M. Yor. Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions
Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 4, 435-465 arXiv

P. Biane. Approximate factorization and concentration for characters of symmetric groups
Internat. Math. Res. Notices 2001, no. 4, 179-192.

1999

H. Bercovici, V. Pata. Stable laws and domains of attraction in free probability theory With an appendix by Philippe Biane.
Ann. of Math. (2) 149 (1999), no. 3, 1023-1060. arXiv

1998

P. Biane. Processes with free increments
Mathematische Zeitschrift 227, 143-174 (1998)

P. Biane. Quantum Markov processes and group representations
Quantum probability communications, 53-72, QP-PQ, X, World Sci. Publ., River Edge, NJ, 1998.

P. Biane. Representations of symmetric groups and free probability
Advances in Mathematics 138, 126-181 (1998)

P. Biane. R. Speicher. Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
Probability Theory and related Fields 112, 373--410 (1998)

1997

P. Biane, Free hypercontractivity
Communications in Mathematical Physics, 184, 457-474 (1997)

P. Biane. On the free convolution with a semi-circular distribution
Indiana Univ. Math. J. 46 (1997), no. 3, 705-718.

P. Biane. Some properties of crossings and partitions
Discrete Math. 175 (1997), no. 1-3, 41-53.

P. Biane. Segal-Bargmann transform, functional calculus on matrix spaces and the theory of semi-circular and circular systems
J. Funct. Anal. 144 (1997), no. 1, 232-286.

P.Biane. Free Brownian motion, free stochastic calculus and random matrices.
Free probability theory (Waterloo, ON, 1995), 1-19, Fields Inst. Commun., 12, Amer. Math. Soc., Providence, RI, 1997.

1996

P. Biane. Minimal factorizations of a cycle and central multiplicative functions on the infinite symmetric group.
Journal of Combinatorial Theory, Series A, 76, 197-212 (1996)

P. Biane. Quelques propriétés du mouvement brownien non-commutatif.
Hommage à P. A. Meyer et J. Neveu. Astérisque No. 236 (1996), 73-101.

1995

P. Biane. Intertwining of Markov semi-groups, some examples.
Séminaire de Probabilités, XXIX, 30-36, Lecture Notes in Math., 1613, Springer, Berlin, 1995.

P. Biane, Calcul stochastique non-commutatif.
Lectures on probability theory (Saint-Flour, 1993), 1-96, Lecture Notes in Math., 1608, Springer, Berlin, 1995.

P. Biane. Permutation model for semi-circular systems and quantum random walks.
Pacific J. Math. 171 (1995), no. 2, 373-387.

P. Biane. Representations of unitary groups and free convolution.
Publ. Res. Inst. Math. Sci. 31 (1995), no. 1, 63-79.

1994

P. Biane. Quelques propriétés du mouvement brownien dans un cone.
Stochastic Process. Appl. 53 (1994), no. 2, 233-240.

P. Biane. Théorème de Ney-Spitzer sur le dual de SU(2).
Trans. Amer. Math. Soc. 345 (1994), no. 1, 179-194.

P. Biane. Some comments on the paper: "Brownian bridge asymptotics for random mappings''.
Random Structures Algorithms 5 (1994), no. 4, 513-516.

1993

P. Biane. Permutations suivant le type d'excédance et le nombre d'inversions et interprétation combinatoire d'une fraction continue de Heine.
European J. Combin. 14 (1993), no. 4, 277-284,

P. Biane. Estimation asymptotique des multiplicités dans les puissances tensorielles d'un g-module.
C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 8, 849-852

P. Biane. Decomposition of Brownian trajectories and some applications.
Probabilities and Statistics. Proceedings of the French-Chinese Wuhan meeting, Wuhan, China,
September 24-October 11, 1990. Pages 51--76. Singapore, World Scientific (1993).

1992

P. Biane. Frontière de Martin du dual de SU(2).
Séminaire de Probabilités, XXVI, 225-233, Lecture Notes in Math., 1526, Springer, Berlin, 1992,

P. Biane. Équation de Choquet-Deny sur le dual d'un groupe compact.
Probab. Theory Related Fields 94 (1992), no. 1, 39-51.

P. Biane. Minuscule weights and random walks on lattices.
Quantum probability & related topics, 51-65, QP-PQ, VII, World Sci. Publ., River Edge, NJ, 1992.

1991

P. Biane. Some properties of quantum Bernoulli random walks.
Quantum probability & related topics, 193-203, QP-PQ, VI, World Sci. Publ., River Edge, NJ, 1991.

P. Biane. Quantum random walk on the dual of SU(n).
Probab. Theory Related Fields 89 (1991), no. 1, 117-129.

1990

P. Biane. Chaotic representation for finite Markov chains.
Stochastics Stochastics Rep. 30 (1990), no. 1, 61-68.

P. Biane. Marches de Bernoulli quantiques.
Séminaire de Probabilités, XXIV, 1988/89, 329-344, Lecture Notes in Math., 1426, Springer, Berlin, 1990.

1989

P. Biane. Comportement asymptotique de certaines fonctionnelles additives de plusieurs mouvements browniens.
Séminaire de Probabilités, XXIII, 198-233, Lecture Notes in Math., 1372, Springer, Berlin, 1989.

1988

P. Biane, M. Yor. Sur la loi des temps locaux browniens pris en un temps exponentiel.
Séminaire de Probabilités, XXII, 454-466, Lecture Notes in Math., 1321, Springer, Berlin, 1988.

P. Biane. Sur un calcul de F. Knight.
Séminaire de Probabilités, XXII, 190-196, Lecture Notes in Math., 1321, Springer, Berlin, 1988.

P. Biane, M. Yor. Quelques précisions sur le méandre brownien.
Bull. Sci. Math. (2) 112 (1988), no. 1, 101-109.

1987

P. Biane, J.-F. Le Gall, M. Yor. Un processus qui ressemble au pont brownien.
Séminaire de Probabilités, XXI, 270-275, Lecture Notes in Math., 1247, Springer, Berlin, 1987.

P. Biane, M. Yor. Variations sur une formule de Paul Lévy.
Ann. Inst. H. Poincaré Probab. Statist. 23 (1987), no. 2, suppl., 359-377.

P. Biane, M. Yor. Valeurs principales associées aux temps locaux browniens.
Bull. Sci. Math. (2) 111 (1987), no. 1, 23-101.

1986

P. Biane. Relations entre pont et excursion du mouvement brownien réel.
Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 1, 1-7.

1985

P. Biane. Comparaison entre temps d'atteinte et temps de séjour de certaines diffusions réelles.
Séminaire de probabilités, XIX, 1983/84, 291-296, Lecture Notes in Math., 1123, Springer, Berlin, 1985.

P. Biane, M. Yor. Valeurs principales associées aux temps locaux browniens et processus stables symétriques.
C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 20, 695-698