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DTSTAMP:20251104T111850Z
DESCRIPTION:Counting lattice walks confined to cones\n\nThe study of lattic
 e walks confined to cones is a very lively topic in combinatorics and in p
 robability theory\, which has witnessed rich developments in the past 20 y
 ears. In a typical problem\, one is given a finite set of allowed steps S 
 in Z^d\, and a cone C in R^d. Clearly\, there are |S|^n walks of length n 
 that start from the origin and take their steps in S. But how many of them
  remain the the cone C?\n\nOne of the motivations for studying such questi
 ons is that lattice walks are ubiquitous in various mathematical fields\, 
 where they encode important classes of objects: in discrete mathematics (p
 ermutations\, trees\, words...)\, in statistical physics (polymers...)\, i
 n probability theory (urns\, branching processes\, systems of queues)\, am
 ong other fields.\n\nThe systematic study of these counting problems start
 ed about 20 years ago. Beforehand\, only sporadic cases had been solved\, 
 with the exception of walks with small steps confined to a Weyl chamber\, 
 for which a general reflection principle had been developed. Since then\, 
 several approaches have been combined to understand how the choice of the 
 steps and of the cone influence the nature of the counting sequence a(n)\,
  or of the the associated series A(t)=\sum a(n) t^n. For instance\, if C i
 s the first quadrant of the plane and S only consists of 'small' steps\, i
 t is now understood when A(t) is rational\, algebraic\, or when it satisfi
 es a linear\, or a non-linear\, differential equation. Even in this simple
  case\, the classification involves tools coming from an attractive variet
 y of fields: algebra on formal power series\, complex analysis\, computer 
 algebra\, differential Galois theory\, to cite just a few. And much remain
 s to be done\, for other cones and sets of steps.\n\nThis series of talks 
 given in the framework of the Aisenstadt chair\, will begin with a survey 
 of this topic. The following two talks will deal respectively with proofs 
 of algebraicicty (and D-algebraicity)\, and with recent progresses on walk
 s with arbitrary steps.\n\n \n\nDATES\n\nMonday\, October 1\, 4:00 pm\n\nT
 uesday\, October 2\, 4:00 pm\n\nWednesday\, October 3\, 4:00 pm\n
DTSTART;VALUE=DATE:20181001
DTEND;VALUE=DATE:20181005
LOCATION:Room 6254\, CA\, Pav. André-Aisenstadt
SUMMARY:Aisenstadt Chair: Mireille Bousquet-Mélou
URL:/mathstat/channels/event/aisenstadt-chair-mireille
 -bousquet-melou-290193
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