scholarly journals Relating Ordinary and Fully Simple Maps via Monotone Hurwitz Numbers

10.37236/8634 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Gaëtan Borot ◽  
Séverin Charbonnier ◽  
Norman Do ◽  
Elba Garcia-Failde
Keyword(s):  
Free Probability ◽  
Direct Relation ◽  
Hurwitz Numbers ◽  
Main Motivation ◽  
Topological Recursion ◽  
Matrix Integrals ◽  
Shed Light

A direct relation between the enumeration of ordinary maps and that of fully simple maps first appeared in the work of the first and last authors. The relation is via monotone Hurwitz numbers and was originally proved using Weingarten calculus for matrix integrals. The goal of this paper is to present two independent proofs that are purely combinatorial and generalise in various directions, such as to the setting of stuffed maps and hypermaps. The main motivation to understand the relation between ordinary and fully simple maps is the fact that it could shed light on fundamental, yet still not well-understood, problems in free probability and topological recursion.

scholarly journals Weighted Hurwitz Numbers and Topological Recursion

2020 ◽  
Vol 375 (1) ◽  
pp. 237-305 ◽  
Author(s):  
A. Alexandrov ◽  
G. Chapuy ◽  
B. Eynard ◽  
J. Harnad
Keyword(s):  
Hurwitz Numbers ◽  
Topological Recursion

scholarly journals Weighted Hurwitz numbers and topological recursion: An overview

2018 ◽  
Vol 59 (8) ◽  
pp. 081102 ◽  
Author(s):  
A. Alexandrov ◽  
G. Chapuy ◽  
B. Eynard ◽  
J. Harnad
Keyword(s):  
Hurwitz Numbers ◽  
Topological Recursion

scholarly journals Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

2017 ◽  
Vol 360 (2) ◽  
pp. 777-826 ◽  
Author(s):  
A. Alexandrov ◽  
G. Chapuy ◽  
B. Eynard ◽  
J. Harnad
Keyword(s):  
Hurwitz Numbers ◽  
Topological Recursion

scholarly journals Topological recursion and a quantum curve for monotone Hurwitz numbers

2017 ◽  
Vol 120 ◽  
pp. 19-36 ◽  
Author(s):  
Norman Do ◽  
Alastair Dyer ◽  
Daniel V. Mathews
Keyword(s):  
Hurwitz Numbers ◽  
Topological Recursion

scholarly journals Chain of matrices, loop equations, and topological recursion

2018 ◽  
Author(s):  
Marco Bertola
Keyword(s):  
External Field ◽  
Random Matrices ◽  
Recursive Solution ◽  
Matrix Integral ◽  
Discrete Surfaces ◽  
Topological Recursion ◽  
Matrix Integrals ◽  
A Chain ◽  
The One ◽  
Definition Of

This article considers the so-called loop equations satisfied by integrals over random matrices coupled in a chain as well as their recursive solution in the perturbative case when the matrices are Hermitian. Random matrices are used in fields such as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces, both of which are based on the analysis of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. The article discusses these two definitions, perturbative and non-perturbative, along with their relationship. It first provides an overview of a matrix integral before comparing convergent and formal matrix integrals. It then describes the loop equations and their solution in the one-matrix model. It also examines matrices coupled in a chain plus external field and concludes with a generalization of the topological recursion.

scholarly journals The Dynamics of Hybridity in Diana Abu Jaber's The Language of Baklava and Life Without a Recipe

2021 ◽  
Vol 4 (6) ◽  
pp. 07-11
Author(s):  
Salsabeel Jamal Said Jaber
Keyword(s):  
Mixed Culture ◽  
The Other ◽  
Arab American ◽  
Main Concern ◽  
Cultural Issues ◽  
Main Motivation ◽  
Cultural Aspects ◽  
Other Hand ◽  
Shed Light ◽  
Culture And Language

This study explores the portrayal of hybridity in Diana Abu Jaber's two memoirs, The Language of Baklava (2005) and Life without a Recipe (2016).  Many researchers have dealt with the cultural issues that are portrayed in Diana Abu Jaber's novels, especially Crescent (2003) and Arabian Jazz (1993).  This study is distinguished from previous studies by focusing on the cultural aspects that are portrayed in Abu Jaber's two memoirs.  The main concern of this study is to shed light on Diana Abu Jaber's contributions to the exploration of the concept of hybridity in her memoirs from many aspects, such as the hybridity of identity and culture.  Furthermore, it highlights the basic differences between the memoirs in portraying the influences of the mixed culture and identity in Diana Abu Jaber's life.  On the other hand, this study tries to explore the influences of mixed parentage of the writer on her writing of the two novels and her depiction of hybridity in identity, culture and language.  Her American mother and her Jordanian father are the main motivation for Abu Jaber to focus on the mixture between Arab- American cultures in her writing.

scholarly journals A matrix model for simple Hurwitz numbers, and topological recursion

2011 ◽  
Vol 61 (2) ◽  
pp. 522-540 ◽  
Author(s):  
Gaëtan Borot ◽  
Bertrand Eynard ◽  
Motohico Mulase ◽  
Brad Safnuk
Keyword(s):  
Matrix Model ◽  
Hurwitz Numbers ◽  
Topological Recursion
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