Advances in Applied Probability
Local limits of spatial inhomogeneous random graphs
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 …
Advances in Applied Probability
Asymptotic normality for $\boldsymbol{m}$-dependent and constrained $\boldsymbol{U}$-statistics, with applications to pattern matching in random strings and permutations
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…
Advances in Applied Probability
The size of a Markovian SIR epidemic given only removal data
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…
Advances in Applied Probability
Thin-ended clusters in percolation in $\mathbb{H}^d$
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…
Advances in Applied Probability
Thin-ended clusters in percolation in $\mathbb{H}^d$
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…
Advances in Applied Probability
Moran models and Wright–Fisher diffusions with selection and mutation in a one-sided random environment
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…
Advances in Applied Probability
An ergodic theorem for asymptotically periodic time-inhomogeneous Markov processes, with application to quasi-stationarity with moving boundaries
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…