2 citations · 3 across the 8 of their papers we have counts for
8 papers
Universal Asymptotics and Exact Enumeration of Eulerian Maps
Ahmad Barhoumi, Roozbeh Gharakhloo, Nathan Hayford
We calculate the asymptotics of the number of connected, labeled, genus Eulerian maps with an arbitrary degree sequence, in the limit as the total number of vertices tends to i…
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…
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…
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: 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…
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…
A Note on Electrified Droplets
Nathan Hayford, Fudong Wang
We give an in-depth analysis of a 1-parameter family of electrified droplets first described in D. Khavinson et. al. (2005). We also investigate a technique for searching for new s…
Around a theorem of F. Dyson and A. Lenard: Energy Equilibria for Point Charge Distributions in Classical Electrostatics
Artem Abanov, Nathan Hayford, Dmitry Khavinson +1
We discuss several results in electrostatics: Onsager's inequality, an extension of Earnshaw's theorem, and a result stemming from the celebrated conjecture of Maxwell on the numbe…