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Let G be a compact separable topological group. When does there exist a probability P such that P P = U ,where U is Haarmeasure and P + U? We show that such square roots exist if and only if G is ...
This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, th...
We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion...
In this paper we study the academician Peng Shige's papers of the nonlinear expectation since 2005. Under this foundation we interpret some theories and resolve several problems of the theory of G-exp...
Abstract: The constant rate birth--death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces `reconstructed trees' whic...
Abstract: In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the i...
Abstract: We derive the asymptotic distribution of the total length $L_n$ of a Beta($2-\alpha,\alpha$)-coalescent tree for $1<\alpha < 2$, starting from $n$ individuals. There are two regimes: If $\al...
In a recent paper Hilhorst (1) illustrated that the q-Fourier transform for q > 1 is not invertible in the space of density functions. Using an invariance principle he constructed a family of densit...
Given a pair (G, a) where G is a finitely presentable group and a is an integer homology class of this group, Gromov defined in [Gro83] a new numerical invariant associated to this pair called systoli...
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees (“Otter trees”), when trees of a given size are taken with equal likelihood. The height of...
A strategy to evaluate the distribution of the largest Schmidt eigenvalue for entangled random pure states of bipartite systems is proposed. We point out that the multiple integral defining the sought...
The non isotropic noncentral elliptical shape distributions via pseudo-Wishart dis-tribution are founded. This way, the classical shape theory is extended to non isotropic case and the normality assum...

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