Related papers: An Aldous--Hoover Theorem for Radon Distributions

Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…

This paper presents a new general formulation of the Radon-Nikodym theorem in the setting of abstract measure theory. We introduce the notion of weak localizability for a measure and show that this property is both necessary and sufficient…

Noticing the similarity between the monotone weak distributive laws combining two layers of nondeterminism in sets and in compact Hausdorff spaces, we study whether the latter law can be obtained automatically as a weak lifting of the…

Let $X_1,...,X_n$ be $n$ independent unbounded real random variables which have common, roughly speaking, light-tailed type distribution. Denote by $S_1^n$ their sum and by $\pi^{a_n}$ the tilted density of $X_1$, where $a_n…

We provide an improved version of the Darling-Erd\"os theorem for sums of i.i.d. random variables with mean zero and finite variance. We extend this result to multidimensional random vectors. Our proof is based on a new strong invariance…

We prove a Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations, which improves a classical result by Crandall and Rabinowitz in the case where basic spaces are Hilbert spaces. Actually, our theorem does not need any…

Let $\xi_1$, $\xi_2$, $\xi_3$ be independent random variables with nonvanishing characteristic functions, and $a_j$, $b_j$ be real numbers such that $a_i/b_i\ne a_j/b_j$ for $i\ne j$. Let $L_1=a_1\xi_1+a_2\xi_2+a_3\xi_3$,…

A seminal theorem due to Weyl states that if (a_n) is any sequence of distinct integers, then, for almost every real number x, the sequence (a_n x) is uniformly distributed modulo one. In particular, for almost every x in the unit interval,…

The generalized parton distributions are non-perturbative objects, which encode information on long distance dynamics in a number of exclusive processes. They are hybrids of conventional parton densities, distribution amplitudes and hadron…

For $\Cal A\subset L^1_{loc}(\Bbb J,X)$ let $\Cal M\Cal A$ consist of all $f\in L^1_{loc}$ with $ M_h f (\cdot):=\frac {1}{h}\int_{0}^{h}f(\cdot +s)\,ds \in \Cal A$ for all $h>0$. Here $X$ is a Banach space, $\Bbb J= (\alpha ,\infty),…

We give a formula for the tail of the distribution of the non-commutative Rademacher series, which generalizes the result that is already available in the commutative case. As a result, we are able to calculate the norm of these series in…

We use the hyperK\"aler geometry define an disc-counting invariants with deformable boundary condition on hyperK\"ahler manifolds. Unlike the reduced Gromov-Witten invariants, these invariants can have non-trivial wall-crossing phenomenon…

We present results concerning when the joint distribution of an exchangeable sequence is determined by the marginal distributions of its partial sums. The question of whether or not this determination occurs was posed by David Aldous. We…

In this paper, we introduce a certain random variable closely related to the value-distribution of the Hurwitz zeta-function with algebraic parameter. We prove a version of the limit theorem, where the limit measure is presented by the law…

We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of…

We give a new proof of the Kat\v{e}tov-Tong theorem. Our strategy is to first prove the theorem for compact Hausdorff spaces, and then extend it to all normal spaces. The key ingredient is how the ring of bounded continuous real-valued…

We show that Mellin moments of generalized parton distributions, given as even polynomials in the skewness parameter, are obtained from the Taylor expansion of light front wave functions. Furthermore, we derive non-standard versions of the…

We study random vectors of the form $(\operatorname {Tr}(A^{(1)}V),...,\operatorname {Tr}(A^{(r)}V))$, where $V$ is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the $A^{(\nu)}$ are…

We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations…

For a Haar-distributed element $H$ of a compact Lie group \(L\), Eric Rains proved that there is a natural number $D = D_L$ such that, for all $d\ge D$, the eigenvalue distribution of $H^d$ is fixed, and Rains described this fixed…