Jacques Justin

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Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields φ and φ) of the 3D φ field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N -vector model, using some new ideas in the context of(More)
In this paper, we study combinatorial and structural properties of a new class of finite and infinite words that are ‘rich’ in palindromes in the utmost sense. A characteristic property of so-called rich words is that all complete returns to any palindromic factor are themselves palindromes. These words encompass the well-known episturmian words, originally(More)
We discuss the large order behaviour and Borel summability of the topological expansion of models of 2D gravity coupled to general (p, q) conformal matter. In a previous work it was proven that at large order k the string susceptibility had a generic akΓ(2k− 12) behaviour. Moreover the constant a, relevant for the problem of Borel summability, was(More)
In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters. After recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words. Some properties of factors are(More)