The loop-soup switching identity and some of its consequences
I will discuss recent and ongoing work about a new switching identity for critical Brownian loop-soups on cable-graphs and their scaling limits. This at first sight surprising property in essence says that in terms of occupation time (or equivalently the associated GFF), conditioning two points to be in the same loop-cluster amounts to adding a random odd number of Brownian excursions between these two points to an otherwise unconditioned configuration of loops (this number of excursion is one in the limit where one point is sent to infinity, or in the continuum limit). I will discuss various aspects and consequences of this result.
Event Timeslots (1)
Monday
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