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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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The distribution of the power of the sum of inner products of two independent complex normal...

If I have $\mathbf x_n=[x_0, x_1,... ,x_K]^T$ and $\mathbf y_n=[y_0, y_2, ..., y_K]^T$, where $x,y\sim\mathcal C\mathcal N(\mathbf 0,\sigma^2\mathbf I)$. What is the distribution of the following in …
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The distribution of the sum of inner products of two independent complex normal vectors

If I have $\mathbf x_n=[x_0, x_1,... ,x_K]^T$ and $\mathbf y_n=[y_0, y_2, ..., y_K]^T$, where $x,y\sim\mathcal C\mathcal N(\mathbf 0,\sigma^2\mathbf I)$. What is the distribution of the following in …