BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Expanding the Critical Intensity of Random Connection Models - Mat
 thew Dickson (University of British Columbia)
DTSTART:20240828T130000Z
DTEND:20240828T140000Z
UID:TALK219751@talks.cam.ac.uk
DESCRIPTION:Random connection models (RCMs) are random graph models where 
 the vertices are given by a Poisson point process with a given intensity\,
  $\\lambda>0$\, and the edges exist independently with a probability that 
 depends upon the relative positions of the two vertices in question. These
  models include ``Poisson blob models"\, such as the Gilbert disc model. A
 s we vary $\\lambda$\, we observe a percolation phase transition at a crit
 ical intensity $\\lambda_c>0$. Finding this critical value is only possibl
 e in very exceptional cases\, so here we use the lace expansion for RCMs (
 as found by Heydenreich\, van der Hofstad\, Last\, and Matzke 2019) to fin
 d a high-dimension asymptotic expansion for the critical intensity. This i
 s based on arXiv:2309.08830 with Markus Heydenreich (Universit{\\"a}t Augs
 burg)
LOCATION:Seminar Room 2\, Newton Institute
END:VEVENT
END:VCALENDAR