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Specif- ically, in [1, 5] it is proven that totally positive (resp., strictly totally positive) ma- trices, that is matrices with all theirs minors greater than or equal to zero
Now return to the probability in the integrand in the last line in (11) and recall the well-known property of Brownian bridges that conditioning a Brownian motion on its arrival at
Given a martingale sequence (fn) (possibly vector valued), there is a martingale (gn) on the probability space [0, 1] N , with respect to the filtration L n, the minimal sigma field
When a new MRCA is established, the relative proportion Y of the new oldest family which contains the immortal line of descent is distributed as a beta (2, 1) .... Notice that Y has
Nevertheless [1] indeed showed that the 1-potential density of an isotropic stable additive process is comparable to the Riesz kernel at 0, and therefore the 1-potential density
Under the same conditions the finite dimensional distributions of the repeat times converge to the arrival times of suitably modified Poisson processes, and random trees derived
Theorem 1 For any d ≥ 1 , there exists a class A of measurable subsets of R d of vc dimension equal to one such that absconv( A ) is rich with respect to all probability measures
(We remind the reader that a set is called totally disconnected if it contains no connected component larger than one point.) The fractals we study are defined as the complement of
