Convolution of probabilities on finite groups
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I was reading a book on group and representation theory and came across the following which I don't understand, I'd appreciate any help. Suppose P and Q are probabilities on a finite group G. Thus $P(s)ge0$ and $sum_s P(s)=1$ . By the convolution $P*Q$ we mean the probability $P*Q(s)=sum_t P(st^{-1})Q(t)$ ; "first pick $t$ from $Q$ , then independently pick $u$ from $P$ and form the product $ut.$ " Note that in general $P*Q ne Q*P$ . EDIT : the first line is standard, but the latter I cant figure.
group-theory finite-groups representation-theory convolution
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edited Dec 6 at 12:07
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