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SUMMARY:Universal distribution of the number of minima for random walks an
 d Lévy flights - Gregory Schehr (CNRS (Centre national de la recherche sc
 ientifique))
DTSTART:20240808T090000Z
DTEND:20240808T100000Z
UID:TALK215689@talks.cam.ac.uk
DESCRIPTION:We compute exactly the full distribution of the number m of lo
 cal minima in a one-dimensional landscape generated by a random walk or a 
 L&eacute\;vy flight. We consider two different ensembles of landscapes\, o
 ne with a fixed number of steps N and the other till the first-passage tim
 e of the random walk to the origin. We show that &nbsp\;the distribution o
 f m is drastically different in the two ensembles (Gaussian in the former 
 case\, &nbsp\;while having a power-law tail with exponent -3/2 in the latt
 er case). However\, the most striking aspect of our results is that\, in e
 ach case\, the distribution is completely universal for all m (and not jus
 t for large m)\, i.e.\, independent of the jump distribution in the random
  walk. This means that the distributions are exactly identical for L&eacut
 e\;vy flights and random walks with finite jump variance. Our analytical r
 esults are in excellent agreement with our numerical simulations. &nbsp\;
LOCATION:External
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