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SUMMARY:Convex Hulls of Higher-Dimensional Random Walks & First-Passage Re
 setting - Julien Randon-Furling (ENS Paris-Saclay)
DTSTART:20241009T140000Z
DTEND:20241009T150000Z
UID:TALK222319@talks.cam.ac.uk
DESCRIPTION:First we focus on the convex hull of a single multidimensional
  random walk\, with iid steps taken from any symmetric\, continuous distri
 bution. We investigate the persistence of vertices and faces on the bounda
 ry of the hull. In particular we show that the corresponding distributions
  are universal\, and follow three regimes closely linked to the Sparre And
 ersen theorem for one dimensional random walks.\n&nbsp\;\nSecond\, we turn
  to the convex hull of several multidimensional Gaussian random walks. Exp
 licit formulas for the expected volume and expected number of faces are de
 rived in terms of the Gaussian persistence probabilities. Special cases in
 clude the already known results about the convex hull of a single Gaussian
  random walk and the d-dimensional Gaussian polytope.\n&nbsp\;\nThird\, in
 dependently from the previous topics\, we present some simple toy models i
 nvolving so-called "first-passage resetting" for Brownian motion.\n&nbsp\;
 \nCo-authors: G. Uribe Bravo (topic 1)\, D. Zaporozhets (topics 1 & 2)\, B
 . de Bruyne (topic 3)\, S. Redner (topic 3)
LOCATION:Seminar Room 2\, Newton Institute
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