42 citations · 260 across the 31 of their papers we have counts for
32 papers
Degenerate systems of three Brownian particles with asymmetric collisions: invariant measure of gaps
Thomas Dreyfus, Jules Flin, Sandro Franceschi
We consider a degenerate system of three Brownian particles undergoing asymmetric collisions. We study the gap process of this system and focus on its invariant measure. The gap pr…
Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
Thomas Dreyfus, Andrew Elvey Price, Kilian Raschel
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in…
Representability of G-functions as rational functions in hypergeometric series
Thomas Dreyfus, Tanguy Rivoal
Fresán and Jossen have given a negative answer to a question of Siegel about the representability of every -function as a polynomial with algebraic coefficients in -functions…
On the product of two generic -Gevrey series
Thomas Dreyfus, Changgui Zhang
In this paper, we consider a -analog of the Borel-Laplace summation process introduced by Fabienne Marotte and the second author. We specifically examine two power series soluti…
Hypertranscendence and linear difference equations, the exponential case
Thomas Dreyfus
In this paper we study meromorphic functions solutions of linear shift difference equations in coefficients in involving the operator , for s…
On the computation of the difference Galois groups of order three equations
Thomas Dreyfus, Marina Poulet
In this paper we consider the problem of computing the difference Galois groups of order three equations for a large class of difference operators including the shift operator (Cas…
Differential Galois Theory and Integration
Thomas Dreyfus, Jacques-Arthur Weil
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illus…
Differential algebraic generating series of weighted walks in the quarter plane
Thomas Dreyfus
In the present paper we study the nature of the trivariate generating series of weighted walks in the quarter plane. Combining the results of this paper to previous ones, we comple…
Algebraic independence and linear difference equations
Boris Adamczewski, Thomas Dreyfus, Charlotte Hardouin +1
We consider pairs of automorphisms acting on fields of Laurent or Puiseux series: pairs of shift operators , of -differ…
On the nature of four models of symmetric walks avoiding a quadrant
Thomas Dreyfus, Amélie Trotignon
We study the nature of the generating series of some models of walks with small steps in the three quarter plane. More precisely, we restrict ourselves to the situation where the g…
Degeneration from difference to differential Okamoto spaces for the sixth Painlevé equation
Thomas Dreyfus, Viktoria Heu
In the current paper we study the -analogue introduced by Jimbo and Sakai of the well known Painlevé VI differential equation. We explain how it can be deduced from a -analog…
On the Kernel curves associated with walks in the quarter plane
Thomas Dreyfus, Charlotte Hardouin, Julien Roques +1
The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel poly…
Hypertranscendence and linear difference equations
Boris Adamczewski, Thomas Dreyfus, Charlotte Hardouin
After Hölder proved his classical theorem about the Gamma function, there has been a whole bunch of results showing that solutions to linear difference equations tend to be hypertr…
Computing the Lie algebra of the differential Galois group: the reducible case
Thomas Dreyfus, Jacques-Arthur Weil
In this paper, we explain how to compute the Lie algebra of the differential Galois group of a reducible linear differential system. We achieve this by showing how to transform a b…
Length derivative of the generating series of walks confined in the quarter plane
Thomas Dreyfus, Charlotte Hardouin
In the present paper, we use difference Galois theory to study the nature of the generating function counting walks with small steps in the quarter plane. These series are trivaria…
Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions
Carlos E. Arreche, Thomas Dreyfus, Julien Roques
We develop general criteria that ensure that any non-zero solution of a given second-order difference equation is differentially transcendental, which apply uniformly in particular…
Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks
Thomas Dreyfus, Kilian Raschel
We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove th…
On the multiple-scale analysis for some linear partial -difference and differential equations with holomorphic coefficients
Thomas Dreyfus, Alberto Lastra, Stéphane Malek
The analytic and formal solutions of certain family of -difference-differential equations under the action of a complex perturbation parameter is considered. The previous study…
On the nature of the generating series of walks in the quarter plane
Thomas Dreyfus, Charlotte Hardouin, Julien Roques +1
In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane.…
Computing solutions of linear Mahler equations
Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas +1
Mahler equations relate evaluations of the same function at iterated th powers of the variable. They arise in particular in the study of automatic sequences and in the compl…
Functional relations of solutions of q-difference equations
Thomas Dreyfus, Charlotte Hardouin, Julien Roques
In this paper, we study the algebraic relations satisfied by the solutions of -difference equations and their transforms with respect to an auxiliary operator. Our main tool is…
Hypertranscendence of solutions of Mahler equations
Thomas Dreyfus, Charlotte Hardouin, Julien Roques
The last years have seen a growing interest from mathematicians in Mahler functions. This class of functions includes the generating series of the automatic sequences. The present…
Real difference Galois theory
Thomas Dreyfus
In this paper, we develop a difference Galois theory in the setting of real fields. After proving the existence and uniqueness of the real Picard-Vessiot extension, we define the r…
Liouville integrability: an effective Morales-Ramis-Simó theorem
Ainhoa Aparicio-Monforte, Thomas Dreyfus, Jacques-Arthur Weil
Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the inte…