Weak galaxy lensing surveys have consistently reported a lower amplitude for the matter fluctuation spectrum, as measured by $S_8$ parameter, than expected in $\Lambda{\rm CDM}$ cosmology favoured $Planck$. However, expansion history follows predictions of $Planck$ to high accuracy, do measurements cosmic microwave background anisotropies. Redshift space distortion also appear be consistent wit...

Let (X,Y) be a mean zero martingale pair, i.e., X and Y possess mean zero and E(YIX) = X a.s.. It has been proved in various ways that (1) there exist stopping times T on Brownian motion {B(t); such that B(T) is distributed like X and is uniformly integrable; and (2) for any such t there exist stopping times i’ such that T I’ a.s., (B(T), B(I’)) is distributed like (X,Y) and {B(tAT’); is unifor...

In this paper we present a solution of the Einstein's boxes paradox by modern Quantum Mechanics in which a notion of density matrix is equivalent to a notion of a quantum state of a system. We use a secondary quantization formalism in the attempt to make a description particularly clear. The aim of this paper is to provide pedagogical help to the students of quantum mechanics.