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BEGIN:VEVENT
DTSTAMP:20251120T101113Z
DTSTART:20251203T150000Z
DTEND:20251203T160000Z
SUMMARY:Probability Seminar: Peter Gracar - Lipschitz cutset for fractal 
 graphs and applications to the spread of infections
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}p17o-mi79u1
 cs-kadd9q
DESCRIPTION:Peter Gracar (University of Leeds) will speak at the Probabil
 ity seminar.\n\n\nTitle:\n\nLipschitz cutset for fractal graphs and appl
 ications to the spread of infections\n\nAbstract: For Bernoulli supercri
 tical percolation on the $d$-dimensional lattice it is well understood t
 hat the infinite component exists “everywhere”. In fact\, it can be show
 n that this component contains as a subset a Lipschitz connected hyper-s
 urface that can be built along any of the  $d-1$ possible canonical hype
 rplanes of $\\mathbb{Z}^d$. In this talk\, we will explain how one can c
 onstruct a set satisfying similar properties on the Sierpi?ski gasket an
 d then show how a multi-scale construction can be used to get its existe
 nce even for highly correlated particle dependent percolation.\n\nMore p
 recisely\, we will consider the fractal Sierpi?ski gasket or carpet grap
 h in dimension $d\\geq 2$\, denoted by $G$. At time $0$\, we place a Poi
 sson point process of particles onto the graph and let them perform inde
 pendent simple random walks\, which in this setting exhibit sub-diffusiv
 e behaviour. We will generalise the concept of particle process dependen
 t Lipschitz percolation to the (coarse graining of the) space-time graph
  $G\\times \\mathbb{R}$\, where the opened/closed state of space-time ce
 lls is measurable with respect to the particle process inside the cell. 
 We will discuss an application of this generalised framework through the
  following: if particles can spread an infection when they share a site 
 of $G$\, and if they recover independently at some rate $\\gamma>0$\, th
 en if $\\gamma$ is sufficiently small\, the infection started with a sin
 gle infected particle survives indefinitely with positive probability.\n
 \n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 2\, Alan Turing Building\, Manchester
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