We introduce a new model of correlated randomly growing graphs and study the fundamental questions detecting correlation estimating aspects structure. The is simple starts with any graphs, such as uniform attachment (UA) or preferential (PA). Given model, pair (G1,G2) grown in two stages: until time t⋆ they are together (i.e., G1=G2), after which grow independently according to underlying growt...

We consider a class of random ergodic averages, containing averages along non–integer sequences. For such Cohen & Cuny obtained uniform universal pointwise convergence for functions in $L^2$ with $\int \max (1,\log (1+|t|)) d\mu _f<\infty$ via estimation trigonometric polynomials. extend this result to satisfying the weaker condition \log _f<\infty$. also prove that holds corresponding smooth...