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SUMMARY:Dieter Mitsche (Université Jean Monnet\, France)
DTSTART:20230220T140000Z
DTEND:20230220T150000Z
DTSTAMP:20260423T024652Z
UID:QM3/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QM3/61/">Tai
 l bounds for detection times in dynamic hyperbolic graphs</a>\nby Dieter M
 itsche (Université Jean Monnet\, France) as part of Quantum Matter meets 
 Maths (IST\, Lisbon)\n\n\nAbstract\nMotivated by Krioukov et al's model of
  random hyperbolic graphs for real-world networks\, and inspired by the an
 alysis of a dynamic model of graphs in Euclidean space by Peres et al.\, w
 e introduce a dynamic model of hyperbolic graphs in which vertices are all
 owed to move according to a Brownian motion maintaining the distribution o
 f vertices in hyperbolic space invariant. For different parameters of the 
 speed of angular and radial motion\, we analyze tail bounds for detection 
 times of a fixed target and obtain a complete picture\, for very different
  regimes\, of how and when the target is detected: as a function of the ti
 me passed\, we characterize the subset of the hyperbolic space where parti
 cles typically detecting the target are initially located. We overcome sev
 eral substantial technical difficulties not present in Euclidean space\, a
 nd provide a complete picture on tail bounds. On the way\, we obtain also 
 new results for the time more general continuous processes with drift and 
 reflecting barrier spent in certain regions\, and we also obtain improved 
 bounds for independent sums of Pareto random variables.\n\nJoint work with
  Marcos Kiwi and Amitai Linker.\n
LOCATION:https://researchseminars.org/talk/QM3/61/
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