# Haut PDF Topological expansion of the chain of matrices

### Topological expansion of the chain of matrices

**The**most famous is

**the**Kontsevich integral, which is

**the**generating function for intersection numbers [33, 24, ...play

**the**role

**of**a regularized discrete space-time. ...

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### Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry

**the**Kodaira-Spencer field theory ...extend

**the**method

**of**[13] was first made in [7], and here in this paper we deeply improve

**the**result

**of**...[7].

**The**aim

**of**...

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### Asymptotic expansion of smooth functions in polynomials in deterministic matrices and iid GUE matrices

**the**large dimension

**expansion**

**of**

**the**moments

**of**Gaussian

**matrices**to compute

**the**Euler characteristic

**of**

**the**moduli space

**of**...in

**the**...

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### Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula

**of**that work are to find

**the**diagrammatic rules for com- puting

**the**free energy to all order in

**the**

**topological**

**expansion**, and also all mixed correlation functions ...

50

### Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry

**the**Kodaira-Spencer field theory ...extend

**the**method

**of**[13] was first made in [7], and here in this paper we deeply improve

**the**result

**of**...[7].

**The**aim

**of**...

60

### Topological expansion of the β-ensemble model and quantum algebraic geometry in the sectorwise approach

**the**loop equations

**of**

**the**β-ensemble model analogously to

**the**solution found for

**the**Hermitian

**matrices**β = ...1,

**the**solution was expressed using

**the**...

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### The topological correctness of PL-approximations of isomanifolds

**the**existence

**of**

**the**isotopy from f −1 (0) to f P L −1 (0), we will apply

**the**implicit function theorem (Theorem 6) to several functions g that are close to f and we will therefore need ...

44

### Free energy topological expansion for the 2-matrix model.

**of**diagrammatic techniques from

**the**1MM to

**the**2MM also points out that

**the**study

**of**

**the**

**chain**

**of**

**matrices**[21] would give a more general ...

32

### On the Stern–Brocot expansion of real numbers

**the**converse, we use

**the**proof

**of**Theorem ...product

**of**

**matrices**L and R; this product has L’s and R’s in ...take

**the**corresponding product f

**of**morphisms (a 7→ a, b ...

27

### Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants.

**the**recursion hypothesis.

**The**fact that

**the**A and B cycle integrals vanish comes from

**the**symmetry x ↔ ...under

**the**symmetry x ↔ y, f is changed to ˜ f and ˜ f is changed to f . ...

38

### Invariants of algebraic curves and topological expansion

**the**associated formal Baker-Hakiezer function ...notion

**of**a τ function associated to an algebraic ...in

**the**litterature [9], and it is not clear whether our definition coincides with other ...

94

### The sinelaw gap probability, Painlevé 5, and asymptotic expansion by the topological recursion

**The**goal

**of**this article is to rederive

**the**connection between

**the**Painlev´ e 5 integrable system and

**the**universal eigenvalues correlation functions

**of**double-scaled ...

39

### Topological expansion in isomorphisms with random walks for matrix valued fields

**TOPOLOGICAL**

**EXPANSION**IN ISOMORPHISMS WITH RANDOM WALKS FOR MATRIX VALUED FIELDS TITUS LUPU ...fields

**of**real symmetric, complex Hermitian or quaternionic Hermitian

**matrices**over an ...

24

### A short overview of the "Topological recursion"

**the**spectral curve happens to be a very simple and natural geometric object from

**the**A-model point

**of**...typically

**the**”most probable shape”

**of**

**the**objects counted in ...

45

### Does the expansion of biofuels encroach on the forest?

**of**

**the**biofuel-deforestation nexus is complex.

**The**impact

**of**biofuels on deforestation through land use change depends primarily on

**the**type

**of**crops used (Gao et ...

45

### Diffusion at the Surface of Topological Insulators

**the**symplectic and unitary universality classes upon breaking time-reversal symmetry has been observed in ultrathin samples

**of**Bi 2 Te 3 [ 16 ...describing

**the**transport properties

**of**...

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### ON TOPOLOGICAL GENERICITY OF THE MODE-LOCKING PHENOMENON

**of**Schr ¨odinger operators. In contrast to

**the**result in [4],

**the**density

**of**mode-locking for dynamically forced maps is true regardless

**of**

**the**range

**of**

**the**...

20

### A topological definition of the Maslov bundle

**of**this bundle in terms

**of**cocycles and tries to make

**the**links with

**the**strictly

**topological**presentation (representation

**of**

**the**fundamental group) proposed by ...

12

### On traces of the Brandt-Eichler matrices

**the**number

**of**elements in R/1rR. For simplicity,

**the**number

**of**principal left ideals in A whose norm is equal to (1rm) will be denoted by L(A, m) (later we return to

**the**notation ...

14

### The Zeckendorf expansion of polynomial sequences

**the**indepence

**of**different digital expansions. For example, in [6]

**the**following property is shown. Suppose that ql, q2 are two coprime integers and fl, f2 qm resp. ...

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