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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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Why Expected squared length of a projected vector on reduced dimensionality coordinates is k/d?

For the proof of Johnson-Lindenstrauss algorithm by Dasgupta and Gupta, they comment in their paper that for a vector $Z \in R^k $, the expected squared length, $E[L]$ (where $L = \|Z\|^2$) of the pro …