1 citations · 3 across the 9 of their papers we have counts for
13 papers
Scaling limit of the heavy-tailed ballistic deposition model with -sticking
Francis Comets, Joseba Dalmau, Santiago Saglietti
Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of and stick to the interface…
Scale-free percolation in continuum space: quenched degree and clustering coefficient
Joseba Dalmau, Michele Salvi
Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in…
Galton-Watson and branching process representations of the normalized Perron-Frobenius eigenvector
Raphaël Cerf, Joseba Dalmau
Let be a primitive matrix and let be its Perron-Frobenius eigenvalue. We give formulas expressing the associated normalized Perron-Frobenius eigenvector as a simple functio…
A probabilistic proof of Perron's theorem
Raphaël Cerf, Joseba Dalmau
We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of…
The Wright--Fisher model for class--dependent fitness landscapes
Joseba Dalmau
We consider a population evolving under mutation and selection. The genotype of an individual is a word of length over a finite alphabet. Mutations occur during reproduction…
Asymptotic behavior of Eigen's quasispecies model
Joseba Dalmau
We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to infinity and the mutation probability goes to 0. A limiting infinite system o…
The quasispecies distribution
Raphaël Cerf, Joseba Dalmau
The quasispecies model was introduced in 1971 by Manfred Eigen to discuss the first stages of life on Earth. It provides an appealing mathematical framework to study the evolution…
A Markov chain representation of the Perron-Frobenius eigenvector
Raphaël Cerf, Joseba Dalmau
We consider the problem of finding the Perron-Frobenius eigenvector of a primitive matrix. Dividing each of the rows of the matrix by the sum of the elements in the row, the result…
Quasispecies on class-dependent fitness landscapes
Raphaël Cerf, Joseba Dalmau
We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to infinity and the mutation probability goes to 0. We give several explicit for…
The distribution of the quasispecies for a Galton--Watson process on the sharp peak landscape
Joseba Dalmau
We study a classical multitype Galton--Watson process with mutation and selection. The individuals are sequences of fixed length over a finite alphabet. On the sharp peak fitness l…
Convergence of a Moran model to Eigen's quasispecies model
Joseba Dalmau
We prove that a Moran model converges in probability to Eigen's quasispecies model in the infinite population limit.
The distribution of the quasispecies for the Wright-Fisher model on the sharp peak landscape
Joseba Dalmau
We consider the classical Wright-Fisher model with mutation and selection. Mutations occur independently in each locus, and selection is performed according to the sharp peak lands…
The distribution of the quasispecies for a Moran model on the sharp peak landscape
Raphaël Cerf, Joseba Dalmau
We consider the Moran model on the sharp peak landscape, in the asymptotic regime studied in [3], where a quasispecies is formed. We find explicitly the distribution of this quasis…