相关论文: A correction to Kallenberg's theorem for jointly e…

In [Fortini et al., Stoch. Proc. Appl. 100 (2002), 147--165] it is demonstrated that a recurrent Markov exchangeable process in the sense of Diaconis and Freedman is essentially a partially exchangeable process in the sense of de Finetti.…

A new type of stochastic dependence for a sequence of random variables is introduced and studied. Precisely, (X_n)_{n\geq 1} is said to be conditionally identically distributed (c.i.d.), with respect to a filtration (G_n)_{n\geq 0}, if it…

We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular,…

We suggest solving the measurement problem by postulating the existence of a special future final boundary condition for the universe. Although this is an extension of the way boundary conditions are usually chosen (in terrestrial…

Formulas for calculating the joint probability of outcomes of measurements performed on mutually non-interacting component systems of a combined system prepared in an entangled state are presented. The formulas are based on non-relativistic…

Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…

Since the 1970s there has been a rich theory of equilibrium states over shift spaces associated to H\"older-continuous real-valued potentials. The construction of equilibrium states associated to matrix-valued potentials is much more…

We argue that the conclusion of Bell theorem, namely, that there must be spatial non-local correlations in certain experimental situations, does not apply to typical individual measurements performed on entangled EPR pairs. Our claim is…

Let $R$ be a finite local ring. We prove a quantitative universality statement for the cokernel of random matrices with i.i.d. entries valued in $R$. Rather than use the moment method, we use the Lindeberg replacement technique. This…

In this article, we analyze an "impossible measurement" scenario presented by Sorkin. This scenario involving a joint measurement on spacelike separated systems in an intermediary region has widely been discussed in the quantum field theory…

We prove local well-posedness of partially periodic and periodic modified KP-I equations, namely for $\partial_t u+(-1)^{\frac{l+1}{2}}\partial^l_x u-\partial_x^{-1}\partial_y^2 u+u^2\partial_x u=0$ in the anisotropic Sobolev space…

In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it the necessary and sufficient conditions of optional Doob decomposition in the discrete case. This…

The problem of combining p-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily…

Drawing from our earlier works on the notion of causality for nonlocal phenomena, we propose and study the extension of the Sorkin--Woolgar relation $K^+$ onto the space of Borel probability measures on a given spacetime. We show that it…

This version corrects a number of mistakes that appeared in the previous draft. In particular, the (EU-LREM) condition is sufficient for existence and uniqueness but not necessary, as we had claimed. We are grateful to P. C. B. Phillips and…

For a finite set $A\subset \mathbb{R}$ and real $\lambda$, let $A+\lambda A:=\{a+\lambda b :\, a,b\in A\}$. Combining a structural theorem of Freiman on sets with small doubling constants together with a discrete analogue of…

A physical system is in local equilibrium if it cannot be distinguished from a global equilibrium by ``infinitesimally localized measurements''. This should be a natural characterization of local equilibrium, but the problem is to give a…

Physicists describe nature using mathematics as the natural language, and for quantum mechanics, it prefers to use complex numbers. However, whether complex numbers are really necessary for the theory has been debated ever since its birth.…

A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of…

Here it is shown that the simplest description of Bell's experiment according to the canon of von Neumann's theory of measurement explicitly assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This…