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DTSTART:20230326T030000
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DTSTAMP:20260424T143457Z
UID:1680101100@ist.ac.at
DTSTART:20230329T164500
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DESCRIPTION:Speaker: Sigurdur Örn Stefansson\nhosted by M. Beiglböck\, N.
  Berestycki\, L. Erdös\, J. Maas\, F. Toninelli\, E. Schertzer\nAbstract:
  Many combinatorial objects may be decomposed in a natural way into an und
 erlying tree whose vertices are identified with structures which we will c
 all decorations. We refer to such objects as decorated trees. A simple exa
 mple is an ordered tree\, whose decorations are linear orderings of size e
 qual to the degree of their corresponding vertex. Another less trivial exa
 mple are so called looptrees\, introduced by Curien and Kortchemski\, wher
 e the decorations are circle graphs of length equal to the degree of their
  corresponding vertex.Random decorated trees appear  in statistical phys
 ics models on random 2D triangulations (and maps in general). Curien and K
 ortchemski showed that random looptrees describe the boundary between comp
 onents in critical percolation on uniform triangulations and there is evid
 ence that this holds for more general models of maps and matter.In this ta
 lk I will introduce a general model of random decorated trees where the un
 derlying tree is a size conditioned branching process whose offspring dist
 ribution is in the domain of attraction of a stable distribution. This imp
 lies that in large trees\, there will be many vertices which have a large 
 degree. Under some suitable conditions on the decorations\, the decorated 
 tree will have a scaling limit and due to the  vertices of large degree 
 the decorations will be present in the limit.The talk is based on arxiv.o
 rg/abs/2205.02968 (https://arxiv.org/abs/2205.02968) which is a joint wor
 k with Delphin Sénizergues and Benedikt Stufler.
LOCATION:Mondi 2 (I01.01.008)\, Central Building\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at 
SUMMARY:Sigurdur Örn Stefansson: Decorated stable trees
URL:https://talks-calendar.ista.ac.at/events/4091
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