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DTSTAMP:20250813T201615Z
DESCRIPTION:Counting lattice walks confined to cones - Part III\n\nThe stud
 y of lattice walks confined to cones is a very lively topic in combinatori
 cs and in probability theory\, which has witnessed rich developments in th
 e past 20 years. In a typical problem\, one is given a finite set of allow
 ed steps S in Z^d\, and a cone C in R^d. Clearly\, there are |S|^n walks o
 f length n that start from the origin and take their steps in S. But how m
 any of them remain the the cone C?\n	\n	One of the motivations for studying 
 such questions is that lattice walks are ubiquitous in various mathematica
 l fields\, where they encode important classes of objects: in discrete mat
 hematics (permutations\, trees\, words...)\, in statistical physics (polym
 ers...)\, in probability theory (urns\, branching processes\, systems of q
 ueues)\, among other fields.The systematic study of these counting problem
 s started about 20 years ago. Beforehand\, only sporadic cases had been so
 lved\, with the exception of walks with small steps confined to a Weyl cha
 mber\, 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 is the first quadrant of the plane and S only consists of 'small' ste
 ps\, it is now understood when A(t) is rational\, algebraic\, or when it s
 atisfies a linear\, or a non-linear\, differential equation. Even in this 
 simple case\, the classification involves tools coming from an attractive 
 variety of fields: algebra on formal power series\, complex analysis\, com
 puter algebra\, differential Galois theory\, to cite just a few. And much 
 remains to be done\, for other cones and sets of steps.This series of talk
 s given in the framework of the Aisenstadt chair\, will begin with a surve
 y of this topic. The following two talks will deal respectively with proof
 s of algebraicicty (and D-algebraicity)\, and with recent progresses on wa
 lks with arbitrary steps.\n
DTSTART:20181003T200000Z
DTEND:20181003T210000Z
LOCATION:room 6254\, CA\, Pav. André-Aisenstadt
SUMMARY:Mireille Bousquet-Mélou\, CNRS\, Université de Bordeaux
URL:/mathstat/channels/event/mireille-bousquet-melou-c
 nrs-universite-de-bordeaux-290202
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