Thomas Krajewski
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View article: Duality of O(<i>N</i>) and <i>Sp</i>(<i>N</i>) random tensor models: tensors with symmetries
Duality of O(<i>N</i>) and <i>Sp</i>(<i>N</i>) random tensor models: tensors with symmetries Open
In a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order. However, the tensor models considered so far…
View article: Double scaling limit of the prismatic tensor model
Double scaling limit of the prismatic tensor model Open
In Giombi et al (2018 Phys. Rev. D 98 105005), a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using the intermediate field method. We explicitly exhibit the next-to-lead…
View article: The SYK model and random tensors: Gaussian universality
The SYK model and random tensors: Gaussian universality Open
International audience
View article: Constructive Matrix Theory for Higher Order Interaction II: Hermitian and Real Symmetric Cases
Constructive Matrix Theory for Higher Order Interaction II: Hermitian and Real Symmetric Cases Open
This paper provides the constructive loop vertex expansion for stable matrix models with (single trace) interactions of arbitrarily high even order in the Hermitian and real symmetric cases. It relies on a new and simpler method which can …
View article: Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model
Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model Open
We study the effect of non-Gaussian average over the random couplings in a\ncomplex version of the celebrated Sachdev-Ye-Kitaev (SYK) model. Using a\nPolchinski-like equation and random tensor Gaussian universality, we show that\nthe effec…
View article: A Tutte Polynomial for Maps
A Tutte Polynomial for Maps Open
We follow the example of Tutte in his construction of the dichromate of a graph ( i.e. the Tutte polynomial) as a unification of the chromatic polynomial and the flow polynomial in order to construct a new polynomial invariant of maps (gra…
View article: Wigner law for matrices with dependent entries—a perturbative approach
Wigner law for matrices with dependent entries—a perturbative approach Open
We show that Wigner semi-circle law holds for Hermitian matrices with\ndependent entries, provided the deviation of the cumulants from the normalised\nGaussian case obeys a simple power law bound in the size of the matrix. To\nestablish th…
View article: A Renormalisation Group Approach to the Universality of Wigner’s Semicircle Law for Random Matrices with Dependent Entries
A Renormalisation Group Approach to the Universality of Wigner’s Semicircle Law for Random Matrices with Dependent Entries Open
We show that if the non-Gaussian part of the cumulants of a random matrix model obeys some scaling bounds in the size of the matrix, then Wigner’s semicircle law holds. This result is derived using the replica technique and an analogue of …
View article: Power counting and scaling for tensor models
Power counting and scaling for tensor models Open
Random tensors are natural generalisations of matrix models related to random geometries of dimension D. Here, we revisit the large N limit of tensor models and the power counting of tensorial group field theories using a renormalisation g…
View article: Exact Renormalisation Group Equations and Loop Equations for Tensor Models
Exact Renormalisation Group Equations and Loop Equations for Tensor Models Open
In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading …
View article: Using Grassmann calculus in combinatorics: Lindström-Gessel-Viennot lemma and Schur functions
Using Grassmann calculus in combinatorics: Lindström-Gessel-Viennot lemma and Schur functions Open
Grassmann (or anti-commuting) variables are extensively used in theoretical physics. In this paper we use Grassmann variable calculus to give new proofs of celebrated combinatorial identities such as the Lindström-Gessel-Viennot formula fo…
View article: Using Grassmann calculus in combinatorics: Lindstr\\"om-Gessel-Viennot\n lemma and Schur functions
Using Grassmann calculus in combinatorics: Lindstr\\"om-Gessel-Viennot\n lemma and Schur functions Open
Grassmann (or anti-commuting) variables are extensively used in theoretical\nphysics. In this paper we use Grassmann variable calculus to give new proofs of\ncelebrated combinatorial identities such as the Lindstr\\"om-Gessel-Viennot\nform…
View article: Renormalization group-like proof of the universality of the Tutte polynomial for matroids
Renormalization group-like proof of the universality of the Tutte polynomial for matroids Open
International audience
View article: Power counting ans scaling for tensor models
Power counting ans scaling for tensor models Open
Random tensors are natural generalisations of matrix models related to random geometries of dimension D. Here, we revisit the large N limit of tensor models and the power counting of tensorial group field theories using a renormalisation g…
View article: Hopf algebras and Tutte polynomials
Hopf algebras and Tutte polynomials Open
By considering Tutte polynomials of Hopf algebras, we show how a Tutte\npolynomial can be canonically associated with combinatorial objects that have\nsome notions of deletion and contraction. We show that several graph\npolynomials from t…
View article: Combinatorial Hopf algebras and topological Tutte polynomials
Combinatorial Hopf algebras and topological Tutte polynomials Open
By considering Tutte polynomials of a combinatorial Hopf algebras, we show how a Tutte polynomial can be canonically associated to a set of combinatorial objects that have some notion of deletion and contraction. We show that numerous grap…
View article: Analyticity results for the cumulants in a random matrix model
Analyticity results for the cumulants in a random matrix model Open
The generating function of the cumulants in random matrix models, as well as the cumulants themselves, can be expanded as asymptotic (divergent) series indexed by maps. While at fixed genus the sums over maps converge, the sums over genera…