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When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such…
We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…
We use deposition models of kinetic roughening of a growing surface to introduce the concepts of universality and scaling and to analyze the qualitative and quantitative role of different parameters. In particular, we focus on two classes…
$\Lambda$-coalescents model genealogies of samples of individuals from a large population by means of a family tree whose branches have lengths. The tree's leaves represent the individuals, and the lengths of the adjacent edges indicate the…
Many research fields, reaching from social networks and epidemiology to biology and physics, have experienced great advance from recent developments in random graphs and network theory. In this paper we propose to view percolation on a…
Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the…
Networks growing according to the rule that every new node has a probability p_k of being attached to k preexisting nodes, have a universal phase diagram and exhibit power law decays of the distribution of cluster sizes in the…
We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first…
Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we…
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…
Constraints on the expansion history of the universe from measurements of cosmological distances make predictions for large-scale structure growth. Since these predictions depend on assumptions about dark energy evolution and spatial…
The existence of universal scaling in the vicinity of the jamming transition of sheared granular materials is predicted by a phenomenology. The critical exponents are explicitly determined, which are independent of the spatial dimension.…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
We consider the complex polymer system, consisting of ring polymer connected to the $f_1$-branched star-like structure, in good solvent in presence of structural inhomogeneities. We assume, that structural defects are correlated at large…
Genomic data are rapidly resolving the tree of living species calibrated to time, the timetree of life, which will provide a framework for research in diverse fields of science. Previous analyses of taxonomically restricted timetrees have…
We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave…
Clusters formed by fluctuations of two-dimensional (2D) directed interfaces around a threshold level have been extensively studied at equilibrium and in nonequilibrium steady states, but their coarsening dynamics remain poorly understood.…
We consider one-dimensional hierarchical coalescence processes (in short HCPs) where two or three neighboring domains can merge. An HCP consists of an infinite sequence of stochastic coalescence processes: each process occurs in a different…
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving…