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

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

**the**hermitian two-

**matrix**

**model**(2MM) solutions have been obtained, at early stages, in

**the**planar limit of

**the**1/N-

**expansion**...that

**the**2MM solution in ...

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

**the**matrices, and could not be computed by standard methods.

**The**first explicit computations were obtained in [4] and ...compute

**the**

**topological**

**expansion**of a family of mixed ...

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

**expansion**of random

**matrix**models has a strong link with algebraic geometry ...[27].

**The**

**free**

**energy**and correlation functions have been computed in terms of properties of an ...

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### Invariants of algebraic curves and topological expansion

**for**curves not coming from

**the**large N limit of

**the**loop equations of a

**matrix**...-

**The**double scaling limit of a

**matrix**...tune

**the**parameters of a

**matrix**...

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### Loop equations for the semiclassical 2-matrix model with hard edges

**the**function eq.

**2**-27 E(x, y) is unchanged under

**the**exchange x ↔ y, V1 ↔ V2, s ↔ ˜ s, which is

**the**generalization of Matytsin’s duality property [17]: X(Y (x)) = x (4-1)

**The**...

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### A matrix model for the topological string II: The spectral curve and mirror geometry

**matrix**

**model**M X and to compare it to

**the**mirror curve S X of ...matrices

**matrix**

**model**with non-polyno- mial potential.

**The**problem of determining

**the**spectral curve of ...

41

### Topological expansion of the chain of matrices

**for**various applications.

**The**most famous is

**the**Kontsevich integral, which is

**the**generating function

**for**intersection numbers [33, 24, ...general

**model**. Multimatrix ...

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### Evaluating the flow stress of aerospace alloys for tube hydroforming process by free expansion testing

**the**tube as a deformable material. In

**the**

**model**, a surface-to-surface contact algorithm was ap- plied to

**the**interface between

**the**tube and

**the**die with Coulomb’s friction ...

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### Rapid prediction of solvation free energy. 2. The first-shell hydration (FiSH) continuum model

**the**benefits of ISCD-dependent Born radii to account

**for**charge asymmetry effects, as well as

**the**improvements afforded by training on real molecules

**for**

**the**nonlinear ...

17

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

**2**? Institut de physique th´ eorique, CEA Saclay, France. 3 Abstract:

**The**goal of this article is to rederive

**the**connection between

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

**the**...

39

### Topological expansion and boundary conditions

**the**possibilities of drawing interfaces (between

**the**+ and - spins of

**the**Ising

**model**) in all possible ...to

**the**so called double-scaling-limit [6, 5], and should be compared with ...

26

### Topological superconductivity in the one-dimensional interacting Creutz model

**the**

**topological**phase diagram

**for**different values of interaction U , combining results from

**the**mean-field analysis and DMRG ...simulations.

**The**agreement between both approaches ...

8

### Free-energy-dissipative schemes for the Oldroyd-B model

**the**paper and results We will show that it is possible to build numerical schemes discretizing

**the**Oldroyd-B system (1)– (

**2**) such that solutions to those discretizations satisfy a

**free**...

57

### 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.

**For**β = 1,

**the**solution was expressed using ...

59

### Master loop equations, free energy and correlations for the chain of matrices.

**the**potential well Vk and is linearly coupled to its neigh- boors Mk−1 and ...thus

**the**chain is open. So far,

**the**problem of

**the**closed chain has remained ...unsolved.

**The**...

56

### Large N expansion of the 2-matrix model, multicut case.

**the**support of

**the**large N average density of eigenvalues of

**the**

**matrix**M 1 is made of g + 1 intervals [a i , b i ], i = 1, ...and

**for**each i, A i is a contour which encloses [a i ...

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

**the**proof of Theorem ...develop

**the**product of traces on

**the**left-hand side of

**the**isomorphism identity, apply Theorem ...recombine

**the**terms to get

**the**right-hand side of ...

24

### Phase structure of topological insulators by lattice strong-coupling expansion

**the**phase structure of

**topological**insulators, described by

**the**boundary between

**the**

**topological**insulator and

**the**normal insulator ...formulate

**the**models of ...

8

### A Matrix Model for the Topological String I: Deriving the Matrix Model

**for**computing

**the**

**topological**string partition function, genus by genus, away from

**the**large radius limit, and without having to solve differential ...by

**the**fact that symplectic ...

36

### Topological model for machining of parts with complex shapes

**2**recovery is associated to transition shapes which generally have low curvature and small ...of

**the**HSM process therefore requires

**the**development of a complex process planning that is very ...

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