From the 1 of 6 linked papers with an AI index.
6 papers
Universal Asymptotics and Exact Enumeration of Eulerian Maps
Ahmad Barhoumi, Roozbeh Gharakhloo, Nathan Hayford
The paper derives universal asymptotic formulas for counting labeled Eulerian maps of any genus with arbitrary degree sequences, and provides an exact enumeration for genus‑1 maps,…
The Ising Model Coupled to 2D Gravity: Critical Partition Function
Maurice Duits, Nathan Hayford, Seung-Yeop Lee
We prove that the differential of the log of the partition function for the -matrix model with quartic interactions converges in a certain double-scaling regime to the different…
Asymptotic Properties of a Special Solution to the (3,4) String Equation
Nathan Hayford
We analyze the asymptotic properties a special solution of the string equation, which appears in the study of the multicritical quartic -matrix model. In particular, we…
The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function
Maurice Duits, Nathan Hayford, Seung-Yeop Lee
We compute the genus 0 free energy for the 2-matrix model with quartic interactions, which acts as a generating function for the Ising model's partition function on a random, 4-reg…
The Painlevé I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy
Mohamad Alameddine, Nathan Hayford, Olivier Marchal
Two approaches to the Painlevé I hierarchy are discussed: the isomonodromic construction based on meromorphic connections, and the minimal models construction based on a reduction…
The Ising Model Coupled to 2D Gravity: Higher-order Painlevé Equations/The String Equation
Nathan Hayford
We study a higher-order Painlevé-type equation, arising as a string equation of the order reduction of the KP hierarchy. This equation appears at the multi-critical point…