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DTSTAMP:20250713T213251Z
DESCRIPTION:Title: An infrared bound for the marked random connection model
 \n\nAbstract: We investigate a spatial random graph model whose vertices a
 re given as a marked Poisson process on Rd. Edges are inserted between any
  pair of points independently with probability depending on the Euclidean 
 distance of the two endpoints and their marks. Upon variation of the Poiss
 on density\, a percolation phase transition occurs under mild conditions: 
 for low density there are finite connected components only\, while for lar
 ge density there is an infinite component almost surely.\n\nOur interest i
 s on the transition between the low- and high-density phase\, where the sy
 stem is critical. We prove that if dimension is high enough and the mark d
 istribution satisfies certain conditions\, then an infrared bound for the 
 critical connection function is valid. This implies the triangle condition
 \, thus indicating mean-field behaviour.\n	We achieve this result through c
 ombining the recently established lace expansion for Poisson processes wit
 h spectral estimates.\n	\n	Based on joint work with Matthew Dickson.\n\nLoca
 tion: \n\n(Hybrid) https://mcgill.zoom.us/j/86314328515?pwd=WnBuci9qNVNST3
 l1OTZUaVNTRlQ0UT09\n\nRoom: André Aisenstadt 6214\n\n \n
DTSTART:20220428T153000Z
DTEND:20220428T163000Z
SUMMARY:Markus Heydenreich
URL:/mathstat/channels/event/markus-heydenreich-339275
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