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DTSTAMP:20260424T041206Z
UID:68270d08096f9122431275@ist.ac.at
DTSTART:20250526T171500
DTEND:20250526T181500
DESCRIPTION:Speaker: Franco Severo\nhosted by Laszlo Erdös\, Jan Maas\nAbs
 tract: Which graphs $G$ admit a percolating phase (i.e. $p_c(G)<1$)? This 
 seemingly simple question is one of the most fundamental ones in percolati
 on theory. A famous argument of Peierls implies that if the number of mini
 mal cutsets of size $n$ from a vertex to infinity in the graph grows at mo
 st exponentially in $n$\, then $p_c(G)<1$. Our first theorem establishes t
 he converse of this statement. This implies\, for instance\, that if a (un
 iformly) percolating phase exists\, then a "strongly percolating one also 
 does. In a second theorem\, we show that if the simple random walk on the 
 graph is uniformly transient\, then the number of minimal cutsets is bound
 ed exponentially (and in particular $p_c<1$). Both proofs rely on a probab
 ilistic method that uses a random set to generate a random minimal cutset 
 whose probability of taking any given value is lower bounded exponentially
  on its size. Joint work with Philip Easo and Vincent Tassion.
LOCATION:Central Bldg / O1 / Mondi 2a (I01.O1.008)\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Franco Severo: Cutsets\, percolation and random walks
URL:https://talks-calendar.ista.ac.at/events/5815
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