BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Firas Rassoul-Agha (Utah)
DTSTART:20211210T173000Z
DTEND:20211210T183000Z
DTSTAMP:20260423T004821Z
UID:PatC/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/48/">Ge
 odesic Length in First-Passage Percolation</a>\nby Firas Rassoul-Agha (Uta
 h) as part of Probability and the City Seminar\n\n\nAbstract\nWe study fir
 st-passage percolation through related optimization problems over paths of
  restricted length. The path length variable is in duality with a shift of
  the weights. This puts into a convex duality framework old observations a
 bout the convergence of the normalized Euclidean length of geodesics due t
 o Hammersley and Welsh\, Smythe and Wierman\, and Kesten\, and leads to ne
 w results about geodesic length and the regularity of the shape function a
 s a function of the weight shift. For points far enough away from the orig
 in\, the ratio of the geodesic length and the $\\ell^1$ distance to the en
 dpoint is uniformly bounded away from one. The shape function is a strictl
 y concave function of the weight shift. Atoms of the weight distribution g
 enerate singularities\, that is\, points of nondifferentiability\, in this
  function. We generalize to all distributions\, directions and dimensions 
 an old singularity result of Steele and Zhang for the planar Bernoulli cas
 e. When the weight distribution has two or more atoms\, a dense set of shi
 fts produce singularities. The results come from a combination of the conv
 ex duality\, the shape theorems of the different first-passage optimizatio
 n problems\, and modification arguments. This is joint work with Arjun Kri
 shnan and Timo Seppalainen.\n
LOCATION:https://researchseminars.org/talk/PatC/48/
END:VEVENT
END:VCALENDAR