Rokhlin's multiple mixing problem in the class of positive local rank actions (Q1576939)

The paper is devoted to the open classical Rohlin's problem -- under what conditions does mixing imply multiple mixing of all orders (\(k\)-fold mixing for all \(k\))? Here the author proves two theorems. Theorem A: Any mixing flow \(T_t\), \(t\in R^n\), \(n\geq 1\) of positive local rank \(\beta(T_t)>0\) is \(k\)-fold mixing for all \(k\). Theorem B: Any mixing action \(T_t\), \(t\in Z^n\), \(n\geq 1\) of local rank \(\beta(T_t)>1/2^n\) is \(k\)-fold mixing for all \(k\).