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SUMMARY:Boundary contacts for reflected random walks in the quarter plane
DTSTART:20260612T083000Z
DTEND:20260612T093000Z
DTSTAMP:20260722T233000Z
UID:indico-event-16405@indico.math.cnrs.fr
DESCRIPTION:Speakers: Việt Hùng Hoàng (Industrial University of Ho Chi
  Minh City)\n\nReflected random walks in the quarter plane arise naturally
  in probability theory\, queueing systems\, statistical physics\, and comb
 inatorics. In this talk\, I will discuss the local time spent on the refle
 ction boundaries. When the drift lies within the cone\, the local time con
 verges\, without normalization\, to a nontrivial random variable as the wa
 lk length tends to infinity. I will present recent results on these limiti
 ng variables in two different settings: in the first\, the reflections on 
 the horizontal and vertical boundaries are assumed to be similar\, leading
  to a recursive structure for the probability mass functions that can be a
 nalyzed using a coupling approach\; in the second\, we consider more gener
 al reflection rules but singular random walks\, for which we derive an exp
 licit closed-form expression for the limiting distribution using the compe
 nsation approach. Some perspectives and simple examples on both singular a
 nd non-singular models will also be discussed\, time permitting. This is j
 oint work with Kilian Rachel.\n\nhttps://indico.math.cnrs.fr/event/16405/
LOCATION:E2 1180 (Tours)
URL:https://indico.math.cnrs.fr/event/16405/
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