Related papers: Intermediate range migration in the two-dimensiona…
We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large…
Most standard descriptions of Type II migration state that massive, gap-opening planets must migrate at the viscous drift rate. This is based on the idea that the disk is separated into an inner and outer region and gas is considered unable…
We study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $\sigma$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
This paper continues the systematic investigation of diffusive shear instabilities initiated in Part I of this series. In this work, we primarily focus on quantifying the impact of non-local mixing, which is not taken into account in Zahn's…
Let $(M,d,\mu)$ be a uniformly discrete metric measure space satisfying space homogeneous volume doubling condition. We consider discrete time Markov chains on $M$ symmetric with respect to $\mu$ and whose one-step transition density is…
When organisms adapt to spatially heterogeneous environments, selection may drive divergence at multiple genes. If populations under divergent selection also exchange migrants, we expect genetic differentiation to be high at selected loci,…
Coalescents with multiple collisions (also called Lambda-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected to a population model with…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…
Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…
We extend previous results due to Ding and Zhuang in order to prove that a phase transition occurs for the long range Ising model in lower dimensions. By making use of a recent argument due to Affonso, Bissacot and Maia from 2022 which…
We consider a population subdivided into two demes connected by migration in which selection acts in opposite direction. We explore the effects of recombination and migration on the maintenance of multilocus polymorphism, on local…
In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the…
In this essay, we recall the specificities of the transition to turbulence in wall-bounded flows and present recent achievements in the understanding of this problem. The transition is abrupt with laminar-turbulent coexistence over a finite…
We investigate a six-species class of May-Leonard models leading to formation two types of competing spatial domains, each one inhabited by three-species with their own internal cyclic rock-paper-scissors dynamics. We study the resulting…
A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The…
Algorithmic stability is among the most potent techniques in generalization analysis. However, its derivation usually requires a stepsize $\eta_t = \mathcal{O}(1/t)$ under non-convex training regimes, where $t$ denotes iterations. This…
The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both…
When estimating a phylogeny from a multiple sequence alignment, researchers often assume the absence of recombination. However, if recombination is present, then tree estimation and all downstream analyses will be impacted, because…