arXiv subjects

Dongfeng Yan

Publications and source records attributed to Dongfeng Yan.

4 recordsLinked to original sources

arXiv2026

The uniform asymptotics for real double Hurwitz numbers with triple ramification II: lower bounds and asymptotics

This is the second of two papers on the uniform asymptotics for real double Hurwitz numbers with triple ramification. Using the modified tropical correspondence theorem established in the first paper of this series, we introduce a combinatorial invariant that serves as a lower bound for real double Hurwitz numbers with triple ramification. We derive a uniform lower bound for the large-degree and large-genus logarithmic asymptotics of these combinatorial invariants. This uniform lower bound yields the following results: (1) We establish a uniform lower bound for the large-degree and large-genus logarithmic asymptotics of real double Hurwitz numbers with triple ramification and their complex analogues. In particular, we provide a partial answer to an open question proposed by Dubrovin, Yang and Zagier on the uniform bound for simple Hurwitz numbers. (2) We prove logarithmic equivalence between real double Hurwitz numbers with triple ramification and their complex analogues as the degree tends to infinity and only simple branch points are added. (3) As the genus tends to infinity and only simple branch points are added, we show that the logarithms of real double Hurwitz numbers with triple ramification and their complex analogues are of the same order.

math.CO↗

arXiv2024

Localization for random operators on $\mathbb{Z}^d$ with the long-range hopping

In this paper, we investigate random operators on $\mathbb{Z}^d$ with H\"older continuously distributed potentials and the long-range hopping. The hopping amplitude decays with the inter-particle distance $\|\bm x\|$ as $e^{-\log^{\rho}(\|\bm x\|+1)}$ with $\rho>1,\bm x\in\Z^d$. By employing the multi-scale analysis (MSA) technique, we prove that for large disorder, the random operators have pure point spectrum with localized eigenfunctions whose decay rate is the same as the hopping term. This gives a partial answer to a conjecture of Yeung and Oono [{\it Europhys. Lett.} 4(9), (1987): 1061-1065].

math-ph↗

arXiv2023

The uniform asymptotics for real double Hurwitz numbers with triple ramification I: the tropical correspondence

This is the first of two papers on the uniform asymptotics for real double Hurwitz numbers with triple ramification. Real double Hurwitz numbers with triple ramification count the number of real ramified coverings of the complex projective line $\mathbb{C}\mathbb{P}^1$ by real Riemann surfaces of genus $g$, where the ramification profiles over $0$ and $\infty$ are $\lambda$ and $\mu$ respectively, and the ramification profiles over the remaining real branch points consist of either $(3,1,\ldots,1)$ or $(2,1,\ldots,1)$. We apply a modified version of the tropical computation framework developed by Markwig and Rau for real Hurwitz numbers (Math. Z. 281 (2015), no. 1-2, 501-522) to compute the real double Hurwitz numbers with triple ramification. The new ingredient in our computation is the application of real simple resolution, a technique that enables us to resolve a triple branch point into a pair of simple branch points. Using real simple resolution, we establish a correspondence between real double Hurwitz numbers with triple ramification and weighted counts of tropical covers. This modified tropical correspondence simplifies the asymptotic analysis of real double Hurwitz numbers with triple ramification.

math.AG↗

arXiv2019

KAM tori for the generalized Bejamin-Bona-Mahony equation

A generalized Benjamin-Bona-Mahony (gBBM) equation subject to the periodic boundary condition is studied in this paper. Based on a new infinite dimensional Kolomogorov-Arnold-Moser (KAM) theorem with normal frequencies of finite limit-points, it is shown that the gBBM equation admits plenty of time-quasi-periodic solutions with two frequencies of high modes.

math.DS↗