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Asymptotic geometry of discrete interlaced patterns: Part IIPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); (English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### National Category

Natural Sciences
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-176649OAI: oai:DiVA.org:kth-176649DiVA: diva2:868186
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt470",{id:"formSmash:j_idt470",widgetVar:"widget_formSmash_j_idt470",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt476",{id:"formSmash:j_idt476",widgetVar:"widget_formSmash_j_idt476",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt483",{id:"formSmash:j_idt483",widgetVar:"widget_formSmash_j_idt483",multiple:true});
##### Funder

Knut and Alice Wallenberg Foundation, 2010.0063
##### Note

##### In thesis

We study the boundary of the liquid region L in large random lozenge tiling models defined by uniform random interlacing particle systems with general initial configuration, which lies on the line (x,1), x∈R≡∂H. We assume that the initial particle configuration converges weakly to a limiting density ϕ(x), 0≤ϕ≤1. The liquid region is given by a homeomorphism WL:L→H, the upper half plane, and we consider the extension of W−1L to H¯¯¯. Part of ∂L is given by a curve, the edge E, parametrized by intervals in ∂H, and this corresponds to points where ϕ is identical to 0 or 1. If 0<ϕ<1, the non-trivial support, there are two cases. Either W−1L(w) has the limit (x,1) as w→x non-tangentially and we have a \emph{regular point}, or we have what we call a singular point. In this case W−1L does not extend continuously to H¯¯¯. Singular points give rise to parts of ∂L not given by E and which can border a frozen region, or be "inside" the liquid region. This shows that in general the boundary of ∂L can be very complicated. We expect that on the singular parts of ∂L we do not get a universal point process like the Airy or the extended Sine kernel point processes. Furthermore, E and the singular parts of ∂L are shocks of the complex Burgers equation.

QC 20151110

Available from: 2015-11-09 Created: 2015-11-09 Last updated: 2015-11-10Bibliographically approved1. On Uniformly Random Discrete Interlacing Systems$(function(){PrimeFaces.cw("OverlayPanel","overlay868196",{id:"formSmash:j_idt761:0:j_idt765",widgetVar:"overlay868196",target:"formSmash:j_idt761:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});