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UID:20250810T233920EDT-8474bEHhN8@132.216.98.100
DTSTAMP:20250811T033920Z
DESCRIPTION:Growth rates of invariant random subgroups in negative curvatur
 e\n\nInvariant random subgroups (IRS) are conjugacy invariant probability 
 measures on the space of subgroups in a given group G. They arise as point
  stabilizers of probability measure preserving actions. Invariant random s
 ubgroups can be regarded as a generalization both of normal subgroups and 
 of lattices. As such\, it is interesting to extend results from the theori
 es of normal subgroups and of lattices to the IRS setting. Jointly with Ar
 ie Levit\, we prove such a result: the critical exponent (exponential grow
 th rate) of an infinite IRS in an isometry group of a Gromov hyperbolic sp
 ace (such as a rank 1 symmetric space\, or a hyperbolic group) is almost s
 urely greater than half the Hausdorff dimension of the boundary. If the su
 bgroup is of divergence type\, we show its critical exponent is in fact eq
 ual to the dimension of the boundary. If G has property (T) we obtain as a
  corollary that an IRS of divergence type must in fact be a lattice. The p
 roof uses ergodic theorems for actions of hyperbolic groups. I will also t
 alk about results about growth rates of normal subgroups of hyperbolic gro
 ups that inspired this work.\n
DTSTART:20181031T190000Z
DTEND:20181031T200000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Ilya Gekhtman\, University of Toronto
URL:/mathstat/channels/event/ilya-gekhtman-university-
 toronto-291081
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