The series of advanced courses initiated in Séminaire de Probabilités XXXIII continues with a course by Ivan Nourdin on Gaussian approximations using Malliavin calculus. The Séminaire also occasionally publishes a series of contributions on a unifying subject; in this spirit, selected participants to the September 2011 Conference on Stochastic Filtrations, held in Strasbourg and organized by Michel Émery, have also contributed to the present volume. The rest of the work covers a wide range of topics, such as stochastic calculus and Markov processes, random matrices and free probability, and combinatorial optimization.

This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs. The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou, M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte, S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.

In addition to its further exploration of the subject of peacocks, introduced in recent Séminaires de Probabilités, this volume continues the series’ focus on current research themes in traditional topics such as stochastic calculus, filtrations and random matrices. Also included are some particularly interesting articles involving harmonic measures, random fields and loop soups. The featured contributors are Mathias Beiglböck, Martin Huesmann and Florian Stebegg, Nicolas Juillet, Gilles Pags, Dai Taguchi, Alexis Devulder, Mátyás Barczy and Peter Kern, I. Bailleul, Jürgen Angst and Camille Tardif, Nicolas Privault, Anita Behme, Alexander Lindner and Makoto Maejima, Cédric Lecouvey and Kilian Raschel, Christophe Profeta and Thomas Simon, O. Khorunzhiy and Songzi Li, Franck Maunoury, Stéphane Laurent, Anna Aksamit and Libo Li, David Applebaum, and Wendelin Werner.

This milestone 50th volume of the "Séminaire de Probabilités" pays tribute with a series of memorial texts to one of its former editors, Jacques Azéma, who passed away in January. The founders of the "Séminaire de Strasbourg", which included Jacques Azéma, probably had no idea of the possible longevity and success of the process they initiated in 1967. Continuing in this long tradition, this volume contains contributions on state-of-art research on Brownian filtrations, stochastic differential equations and their applications, regularity structures, quantum diffusion, interlacing diffusions, mod-Ø convergence, Markov soup, stochastic billiards and other current streams of research.

This volume is dedicated to the memory of Marc Yor, who passed away in 2014. The invited contributions by his collaborators and former students bear testament to the value and diversity of his work and of his research focus, which covered broad areas of probability theory. The volume also provides personal recollections about him, and an article on his essential role concerning the Doeblin documents. With contributions by P. Salminen, J-Y. Yen & M. Yor; J. Warren; T. Funaki; J. Pitman& W. Tang; J-F. Le Gall; L. Alili, P. Graczyk & T. Zak; K. Yano & Y. Yano; D. Bakry & O. Zribi; A. Aksamit, T. Choulli & M. Jeanblanc; J. Pitman; J. Obloj, P. Spoida & N. Touzi; P. Biane; J. Najnudel; P. Fitzsimmons, Y. Le Jan & J. Rosen; L.C.G. Rogers & M. Duembgen; E. Azmoodeh, G. Peccati & G. Poly, timP-L Méliot, A. Nikeghbali; P. Baldi; N. Demni, A. Rouault & M. Zani; N. O'Connell; N. Ikeda & H. Matsumoto; A. Comtet & Y. Tourigny; P. Bougerol; L. Chaumont; L. Devroye & G. Letac; D. Stroock and M. Emery.

This 49th volume offers a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France. This includes articles on latest developments on diffusion processes, large deviations, martingale theory, quasi-stationary distribution, random matrices, and many more. All the contributions come from spontaneous submissions and their diversity illustrates the good health of this branch of mathematics. The featured contributors are E. Boissard, F. Bouguet, J. Brossard, M. Capitaine, P. Cattiaux, N. Champagnat, K. Abdoulaye Coulibaly-Pasquier, H. Elad Altman, A. Guillin, P. Kratz, A. Lejay, C. Leuridan, P. McGill, L. Miclo, G. Pagès, E. Pardoux, P. Petit, B. Rajeev, L. Serlet, H. Tsukada, D. Villeomannais and B. Wilbertz.

Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.