Consider a set of n vertices, where each vertex has a location in that is sampled uniformly from the unit cube in , and a weight associated to it. Construct a random graph by placing edges independently for each vertex pair with a probability that is …
We study (asymmetric) -statistics based on a stationary sequence of -dependent variables; moreover, we consider constrained -statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps between indices. Resul…
During an epidemic outbreak, typically only partial information about the outbreak is known. A common scenario is that the infection times of individuals are unknown, but individuals, on displaying symptoms, are identified as infectious and removed fro…
Consider Bernoulli bond percolation on a graph nicely embedded in hyperbolic space
in such a way that it admits a transitive action by isometries of
. Let
be the supremum of all percolation parameters such that no point at infinity o…
Consider Bernoulli bond percolation on a graph nicely embedded in hyperbolic space
in such a way that it admits a transitive action by isometries of
. Let
be the supremum of all percolation parameters such that no point at infinity o…
Consider a two-type Moran population of size N with selection and mutation, where the selective advantage of the fit individuals is amplified at extreme environmental conditions. Assume selection and mutation are weak with respect to N, and extreme env…
This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded function f, the time…
This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded function f, the time…
We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of order . The corresponding equation turns out to have a unique solution that, depending on a particular shape of the drift, either stays above som…