Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Morters, Peter"'
Preferential attachment networks with power law exponent $\tau>3$ are known to exhibit a phase transition. There is a value $\rho_{\rm c}>0$ such that, for small edge densities $\rho\leq \rho_c$ every component of the graph comprises an asymptoticall
Externí odkaz:
http://arxiv.org/abs/1712.00400
Autor:
Morters, Peter, Redl, Istvan
An unbiased shift of the two-sided Brownian motion $(B_t \colon t\in{\mathbb R})$ is a random time $T$ such that $(B_{T+t} \colon t\in{\mathbb R})$ is still a two-sided Brownian motion. Given a pair $\mu, \nu$ of orthogonal probability measures, an u
Externí odkaz:
http://arxiv.org/abs/1605.07529
We study a class of branching processes in which a population consists of immortal individuals equipped with a fitness value. Individuals produce offspring with a rate given by their fitness, and offspring may either belong to the same family, sharin
Externí odkaz:
http://arxiv.org/abs/1601.08128
Autor:
Jacob, Emmanuel, Morters, Peter
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the $d$-dimensio
Externí odkaz:
http://arxiv.org/abs/1504.00618
Autor:
Morters, Peter, Redl, Istvan
Let $(X_n \colon n\in\Z)$ be a two-sided recurrent Markov chain with fixed initial state $X_0$ and let $\nu$ be a probability measure on its state space. We give a necessary and sufficient criterion for the existence of a non-randomized time $T$ such
Externí odkaz:
http://arxiv.org/abs/1407.4734
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\eps$, agrees up to generation $K$ with a regular $\mu$-ary tree, where $\mu$ is the essential minimum of the offspring distribution and the random v
Externí odkaz:
http://arxiv.org/abs/1204.3080
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\eps$, converges as $\eps\downarrow 0$ in law to the regular $\mu$-ary tree, where $\mu$ is the essential minimum of the offspring distribution. This
Externí odkaz:
http://arxiv.org/abs/1006.2315
Autor:
Kiefer, Richard, Morters, Peter
The frontier of a planar Brownian motion is the boundary of the unbounded component of the complement of its range. In this paper we find the Hausdorff dimension of the set of double points on the frontier.
Comment: 15 pages, 3 figures
Comment: 15 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/0808.0425
Autor:
Dereich, Steffen, Morters, Peter
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and then have
Externí odkaz:
http://arxiv.org/abs/0807.4904
Autor:
Morters, Peter, Ortgiese, Marcel
We consider a model of directed polymers on a regular tree with a disorder given by independent, identically distributed weights attached to the vertices. For suitable weight distributions this model undergoes a phase transition with respect to its l
Externí odkaz:
http://arxiv.org/abs/0806.3430