English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this article, we show that the double scaling limit correlation functionsof a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when$y\sim x^{2m}$ for arbitrary values of the integer $m$) are the same as thedeterminantal formulae defined by conformal $(2m,1)$ models. Our approachfollows the one developed by Berg\`{e}re and Eynard in \cite{BergereEynard} anduses a Lax pair representation of the conformal $(2m,1)$ models (givingPainlev\'e II integrable hierarchy) as suggested by Bleher and Eynard in\cite{BleherEynard}. In particular we define Baker-Akhiezer functionsassociated to the Lax pair to construct a kernel which is then used to computedeterminantal formulae giving the correlation functions of the double scalinglimit of a matrix model near the merging of two cuts.

Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case