20 Boxplots of the estimated probability, ψ, of a carcass falling in the searched area. Boxes represent the IQR with median. Whiskers mark the 95% and 99% CIs. Figure drawn using the plot function from the dwp package with the estimated ψ's: plot(psi01). . . . . . . . . 21 Comparison of box plots of the estimated probabilities, ψ, of a carcass falling in the searched area according to the xep01 (black) and xep02 (red) models. Boxes represent the IQR with median.
We prove a probabilistic generalization of the classic result that infinite power towers, c c . . ., converge if and only if c ∈ [e −e , e 1/e ]. Given an i.i.d. sequence {A i } i∈N , we find that convergence of the power towerIt is natural to view this type of sequence as repeated iteration of a function, in this case MSC2020 subject classifications: 60J05.
For each $n>0$ there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations “conjugated by $z \to z^n$”. We show that these families are free of relations, which determines the structure of “the group of homeomorphisms of finite type”. We next consider factorization for more robust groups of homeomorphisms. We refer to this as root subgroup factorization (because the factors correspond to root subgroups). We are especially interested in how root subgroup factorization is related to triangular factorization (i.e., conformal welding) and correspondences between smoothness properties of the homeomorphisms and decay properties of the root subgroup parameters. This leads to interesting comparisons with Fourier series and the theory of Verblunsky coefficients.
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