78 citations · 178 across the 13 of their papers we have counts for
13 papers
On a coalescence process and its branching genealogy
Nicolas Grosjean, Thierry Huillet
We define and analyze a coalescent process as a recursive box-filling process whose genealogy is given by an ancestral time-reversed, time-inhomogeneous Bienyamé-Galton-Watson proc…
On the genealogy and coalescence times of Bienaymé-Galton-Watson branching processes
Nicolas Grosjean, Thierry Huillet
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus o…
Wright-fisher-like models with constant population size on average
Nicolas Grosjean, Thierry Huillet
We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant…
Some Combinatorial Aspects of Discrete Non-linear Population Dynamics
Nicolas Grosjean, Thierry Huillet
Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carle…
Additional aspects of the generalized linear-fractional branching process
Nicolas Grosjean, Thierry Huillet
We derive some additional results on the Bienyamé-Galton-Watson branching process with linear fractional branching mechanism, as studied in \cite{Sag}. This includes: the expli…
On discrete evolutionary dynamics driven by quadratic interactions
Nicolas Grosjean, Thierry Huillet, Geneviève Rollet
After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more speci…
Deterministic versus stochastic aspects of superexponential population growth models
Nicolas Grosjean, Thierry Huillet
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time ex…
Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
J. Avan, S. Belliard, N. Grosjean +1
In this paper, we prove the off-shell equation satisfied by the transfer matrix associated with the XXZ spin- chain on the segment with two generic integrable boundaries a…
Did the ever dead outnumber the living and when? A birth-and-death approach
Jean Avan, Nicolas Grosjean, Thierry Huillet
This paper is an attempt to formalize analytically the question raised in "World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?" Huffington Post, \cite{HJ}.…
On the spread of a branching Brownian motion whose offspring number has infinite variance
Jean Avan, Nicolas Grosjean, Thierry Huillet
We study the impact on shape parameters of an underlying Bienaymé-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanis…
On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
N. Grosjean, J. M. Maillet, G. Niccoli
We consider general cyclic representations of the 6-vertex Yang-Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov-Stroganov model and the correspon…
The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
N. Grosjean, G. Niccoli
The most general cyclic representations of the quantum integrable tau_2-model are analyzed. The complete characterization of the tau_2-spectrum (eigenvalues and eigenstates) is ach…
On the form factors of local operators in the lattice sine-Gordon model
N. Grosjean, J. M. Maillet, G. Niccoli
We develop a method for computing form factors of local operators in the framework of Sklyanin's separation of variables (SOV) approach to quantum integrable systems. For that purp…