Section: New Results
Random Walks in Orthants
Participant : Guy Fayolle.
The Second Edition of the Book  Random walks in the Quarter Plane, prepared in collaboration with R. Iasnogorodski (St-Petersburg, Russia) and V. Malyshev (MGU, Moscow), has been published by Springer in the collection Probability Theory and Stochastic Processes.
Part II of this second edition borrows specific case-studies from queueing theory and enumerative combinatorics. Five chapters have been added, including examples and applications of the general theory to enumerative combinatorics. Among them:
Chapter Counting Lattice Walks concerns the so-called enumerative combinatorics. When counting random walks with small steps, the nature (rational, algebraic or holonomic) of the generating functions can be found and a precise classification is given for the basic (up to symmetries) 79 possible walks.