Higher-order Airy scaling in deformed Dyck paths

Nils Haug, Adri Olde Daalhuis, Thomas Prellberg

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We introduce a deformed version of Dyck paths (DDP), where additional to the steps allowed for Dyck paths, ‘jumps’ orthogonal to the preferred direction of the path are permitted. We consider the generating function of DDP, weighted with respect to their half-length, area and number of jumps. This represents the first example of an exactly solvable two-dimensional lattice vesicle model showing a higher-order multicritical point. Applying the generalized method of steepest descents, we see that the associated two-variable scaling function is given by the logarithmic derivative of a generalized (higher-order) Airy integral.
Original languageEnglish
Pages (from-to)1193-1208
Number of pages16
JournalJournal of Statistical Physics
Volume166
Issue number5
Early online date3 Jan 2017
DOIs
Publication statusPublished - Mar 2017

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