uu.seUppsala University Publications

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Asymptotics for a special solution of the thirty fourth Painleve equationPrimeFaces.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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2009 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 22, no 7, 1523-1558 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2009. Vol. 22, no 7, 1523-1558 p.
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-128993DOI: 10.1088/0951-7715/22/7/002ISI: 000266916100003OAI: oai:DiVA.org:uu-128993DiVA: diva2:332418
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt375",{id:"formSmash:j_idt375",widgetVar:"widget_formSmash_j_idt375",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt381",{id:"formSmash:j_idt381",widgetVar:"widget_formSmash_j_idt381",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2016-05-13Bibliographically approved

In a previous paper we studied the double scaling limit of unitary random matrix ensembles of the form Z(n,N)(-1) vertical bar det M vertical bar(2 alpha)e(-NTrV(M)) dM with alpha > -1/2. The factor vertical bar det M vertical bar(2 alpha) induces critical eigenvalue behaviour near the origin. Under the assumption that the limiting mean eigenvalue density associated with V is regular, and that the origin is a right endpoint of its support, we computed the limiting eigenvalue correlation kernel in the double scaling limit as n, N -> infinity such that n(2/3)(n/N - 1) = O(1) by using the Deift-Zhou steepest descent method for the Riemann-Hilbert problem for polynomials on the line orthogonal with respect to the weight vertical bar x vertical bar(2 alpha)e(-NV(x)). Our main attention was on the construction of a local parametrix near the origin by means of the psi-functions associated with a distinguished solution u(alpha) of the Painleve XXXIV equation. This solution is related to a particular solution of the Painleve II equation, which, however, is different from the usual Hastings-McLeod solution. In this paper we compute the asymptotic behaviour of u(alpha)(s) as s -> +/-infinity. We conjecture that this asymptotics characterizes u(alpha) and we present supporting arguments based on the asymptotic analysis of a one-parameter family of solutions of the Painleve XXXIV equation which includes u(alpha). We identify this family as the family of tronquee solutions of the thirty fourth Painleve equation.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1080",{id:"formSmash:lower:j_idt1080",widgetVar:"widget_formSmash_lower_j_idt1080",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1081_j_idt1083",{id:"formSmash:lower:j_idt1081:j_idt1083",widgetVar:"widget_formSmash_lower_j_idt1081_j_idt1083",target:"formSmash:lower:j_idt1081:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});