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UID:20251220T070726EST-5707mjXjuN@132.216.98.100
DTSTAMP:20251220T120726Z
DESCRIPTION:Counting lattice walks confined to cones - Part II\n\nThe study
  of lattice walks confined to cones is a very lively topic in combinatoric
 s and in probability theory\, which has witnessed rich developments in the
  past 20 years. In a typical problem\, one is given a finite set of allowe
 d 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 ma
 ny of them remain the the cone C?\n	\n	One of the motivations for studying s
 uch questions is that lattice walks are ubiquitous in various mathematical
  fields\, where they encode important classes of objects: in discrete math
 ematics (permutations\, trees\, words...)\, in statistical physics (polyme
 rs...)\, in probability theory (urns\, branching processes\, systems of qu
 eues)\, among other fields.The systematic study of these counting problems
  started about 20 years ago. Beforehand\, only sporadic cases had been sol
 ved\, with the exception of walks with small steps confined to a Weyl cham
 ber\, for which a general reflection principle had been developed. Since t
 hen\, several approaches have been combined to understand how the choice o
 f 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\, i
 f C is the first quadrant of the plane and S only consists of 'small' step
 s\, it is now understood when A(t) is rational\, algebraic\, or when it sa
 tisfies a linear\, or a non-linear\, differential equation. Even in this s
 imple case\, the classification involves tools coming from an attractive v
 ariety of fields: algebra on formal power series\, complex analysis\, comp
 uter algebra\, differential Galois theory\, to cite just a few. And much r
 emains to be done\, for other cones and sets of steps.This 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 wal
 ks with arbitrary steps.\n
DTSTART:20181002T200000Z
DTEND:20181002T210000Z
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-290201
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