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Here we generalize these results, with appropriate modifications, to a much wider class of random processes generating elements of $F_N$. We introduce the notion of a ''$(M,\\lambda, \\epsilon)$-minimal\" conjugacy class $[w]$ in $F_N$, where $M\\ge 1, \\lambda>1$ and $0<\\epsilon<1$. 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Here we generalize these results, with appropriate modifications, to a much wider class of random processes generating elements of $F_N$. We introduce the notion of a ''$(M,\\lambda, \\epsilon)$-minimal\" conjugacy class $[w]$ in $F_N$, where $M\\ge 1, \\lambda>1$ and $0<\\epsilon<1$. 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