BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:8587@i2m.univ-amu.fr DTSTART;TZID=Europe/Paris:20250422T143000 DTEND;TZID=Europe/Paris:20250422T153000 DTSTAMP:20250317T075247Z URL:https://www.i2m.univ-amu.fr/evenements/tba-214/ SUMMARY:Franco SEVERO (Institut Camille Jordan\, Univ. Lyon 1): Cutsets\, p ercolation and random walk DESCRIPTION:Franco SEVERO: Which graphs $G$ admit a percolating phase (i.e. $p_c(G)<\;1$)? This seemingly simple question is one of the most fundam ental ones in percolation theory. A famous argument due to Peierls implies that if the number of minimal cutsets of size $n$ from a vertex to infini ty in the graph grows at most exponentially in $n$\, then $p_c(G)<\;1$. Our first theorem establishes the converse of this statement. This implies \, for instance\, that if a (uniformly) percolating phase exists\, then a "strongly percolating” one also does. In a second theorem\, we show tha t if the simple random walk on the graph is uniformly transient\, then the number of minimal cutsets is bounded exponentially (and in particular $p_ c<\;1$). Both proofs rely on a probabilistic method that uses a random s et to generate a random minimal cutset whose probability of taking any giv en value is lower bounded exponentially on its size.\nBased on a joint wor k with Philip Easo and Vincent Tassion. CATEGORIES:Séminaire,ALEA,Probabilités LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc e X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0 END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:DAYLIGHT DTSTART:20250330T030000 TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST END:DAYLIGHT END:VTIMEZONE END:VCALENDAR