Related papers: Rapidity gaps and ancestry
We point out an analogy between diffractive electron-nucleus scattering events, and realizations of one-dimensional branching random walks selected according to the height of the genealogical tree of the particles near their boundaries.…
We report on our recent observation that the occurrence of diffractive patterns in the scattering of electrons off nuclei obeys the same law as the fluctuations of the height of genealogical trees in branching diffusion processes.
We propose a partonic picture for high-mass diffractive dissociation events in onium-nucleus scattering, which leads to simple and robust predictions for the distribution of the sizes of gaps in diffractive dissociation of virtual photons…
Results on the behaviour of the rightmost particle in the $n$th generation in the branching random walk are reviewed and the phenomenon of anomalous spreading speeds, noticed recently in related deterministic models, is considered. The…
We present a partonic picture for diffractive onium-nucleus scattering in the large-number-of-color limit from which the distribution of rapidity gaps in a certain kinematic region can be deduced. This picture allows us to draw a parallel…
We consider the range $R^{(n)}$, the tree made up of visited vertices by a diffusive null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree $\mathbb{T}$ up to the $n$-th return time to its root and we consider the…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
We study diffractive scattering cross sections, focusing on the rapidity gap distribution in realistic kinematics at future electron-ion colliders. Our study consists in numerical solutions of the QCD evolution equations in both fixed and…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
This paper gives conditions for the rightmost particle in the $n$th generation of a multitype branching random walk to have a speed, in the sense that its location divided by n converges to a constant as n goes to infinity. Furthermore, a…
Inferences about the evolution of continuous traits based on reconstruction of ancestral states has often been considered more error-prone than analysis of independent contrasts. Here we show that both methods in fact yield identical…
In this thesis, we study the detailed partonic content of the quantum states of a quark-antiquark color dipole subject to high-energy evolution, which are represented by a set of dipoles generated by a stochastic binary branching process,…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…