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SUMMARY:Minimum-Weight Path in a Sparse Erdős--Rényi Graph with Signed W
 eights
DTSTART:20251104T085000Z
DTEND:20251104T095000Z
DTSTAMP:20260717T141100Z
UID:indico-event-15311@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pascal Maillard (IMT)\n\nWe consider a sparse Erdős
 –Rényi graph G(n\,λ/n) where each edge is assigned a random and indepe
 ndent signed weight. For two uniformly chosen vertices\, we study the join
 t distribution of the total weights and hopcounts (number of edges) of the
  near-minimum weight paths connecting them. Under certain conditions on th
 e weight distribution\, we prove that the point process formed by the resc
 aled pairs of total weight and hopcount\, converges weakly to a Poisson po
 int process with a random intensity. This random intensity is characterize
 d by the product of two independent copies of the Biggins martingale limit
  of certain branching random walk. This result generalizes the work of Dal
 y\, Schulte\, and Shneer (Arxiv 2308.12149) from non-negative to signed we
 ights. Joint work with Heng Ma (Technion).\n\nhttps://indico.math.cnrs.fr/
 event/15311/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/15311/
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