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TZOFFSETFROM:+0200
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DTSTART:20180325T010000
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DTSTART:20181028T010000
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DTSTART;TZID=Europe/Helsinki:20180523T134500
DTEND;TZID=Europe/Helsinki:20180523T141500
DTSTAMP:20230128T123205
CREATED:20180523T135055Z
LAST-MODIFIED:20190510T112025Z
UID:9515-1527083100-1527084900@www.csh.ac.at
SUMMARY:"Asymptotics and scaling properties of two-dimensional lattice paths and polygons"
DESCRIPTION:[vc_row][vc_column width=”1/6″][/vc_column][vc_column width=”2/3″][vc_column_text] \nNils Haug will talk at “Combinatorics 2018”\, a conference of the Max Planck Institute for Mathematics in the Sciences.\n \nAsymptotics and scaling properties of two-dimensional lattice paths and polygons\n\n\n \nAbstract\n\n \nWe consider the generating functions of different models of two-dimensional lattice polygons\, weighted with respect to their area and perimeter. Many of them are expected to show similar asymptotic features which do not depend on the exact details of the model\, such as the existence of a scaling limit\, which is described by the Airy function. For rooted self-avoiding polygons\, this scaling behaviour has been conjectured by Guttmann\, Richard and Jensen. However\, a proof of it seems to be currently out of reach. \n \nOne can make progress by considering models which are analytically more tractable\, such as area-weighted Dyck paths. In this talk I will show how a uniform asymptotic expression for their area-perimeter generating function can be obtained by using the method of steepest descents\, generalised to the case of two coalescing saddle points. Afterwards I will explain how a new type of asymptotic behaviour can be observed by adding a perturbation to the area-perimeter generating function of Dyck paths\, leading to a model which we call deformed Dyck paths.[/vc_column_text][/vc_column][vc_column width=”1/6″][/vc_column][/vc_row][vc_row][vc_column][vc_empty_space][/vc_column][/vc_row]
URL:https://www.csh.ac.at/event/nils-haug-asymptotics-scaling-properties-two-dimensional-lattice-paths-polygons/
LOCATION:MPI für Mathematik in den Naturwissenschaften Leipzig\, Inselstraße 22\, Leipzig\, 04103\, Germany
CATEGORIES:Out of House Talks |
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