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UID:6572@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210122T110000
DTEND;TZID=Europe/Paris:20210122T120000
DTSTAMP:20241120T201743Z
URL:https://www.i2m.univ-amu.fr/evenements/spatial-tightness-at-the-edge-o
 f-gibbsian-line-ensembles-guillaume-barraquand/
SUMMARY:Guillaume Barraquand (LPENS\, CNRS\, ENS Paris): Spatial tightness 
 at the edge of Gibbsian line ensembles  - Guillaume Barraquand
DESCRIPTION:Guillaume Barraquand: Consider a sequence of Gibbsian line ense
 mble whose lowest labeled curve (i.e.\, the edge) has tight one-point marg
 inals. Then\, given certain technical assumptions on the nature of the Gib
 bs property and underlying random walk measure\, we prove that the entire 
 spatial process of the edge is tight. We then apply this black-box theory 
 to the log-gamma polymer Gibbsian line ensemble which we construct. The ed
 ge of this line ensemble is the transversal free energy process for the po
 lymer\, and our theorem implies tightness with the ubiquitous KPZ class 2/
 3 exponent\, as well as Brownian absolute continuity of all the subsequent
 ial limits. A key technical innovation which fuels our general result is t
 he construction of a continuous grand monotone coupling of Gibbsian line e
 nsembles with respect to their boundary data (entrance and exit values\, a
 nd bounding curves). {\\em Continuous} means that the Gibbs measure varies
  continuously with respect to varying the boundary data\, {\\em grand} mea
 ns that all uncountably many boundary data measures are coupled to the sam
 e probability space\, and {\\em monotone} means that raising the values of
  the boundary data likewise raises the associated measure. This result app
 lies to a general class of Gibbsian line ensembles where the underlying ra
 ndom walk measure is discrete time\, continuous valued and log-convex\, an
 d the interaction Hamiltonian is nearest neighbor and convex.\nJoint work 
 with Ivan Corwin\, Evgeni Dimitrov\n\nhttps://arxiv.org/abs/2101.03045\n\n
 &nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/01/Guillaume_Barraquand.jpg
CATEGORIES:Séminaire,Probabilités
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