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Limit theorems for radial random walks on Euclidean spaces of high dimensions
Let be a fixed probability measure. For each
dimension , let be i.i.d.
-valued random variables with radially symmetric distributions
and radial distribution . We investigate the distribution of the Euclidean
length of for large parameters and .
Depending on the growth of the dimension we derive by the method of
moments two complementary CLT's for the functional with normal
limits, namely for and . Moreover, we present a
CLT for the case . Thereby we derive explicit
formulas and asymptotic results for moments of radial distributed random
variables on \b R^p.
All limit theorems are considered also for orthogonal invariant random walks
on the space \b M_{p,q}(\b R) of matrices instead of \b R^p for
and some fixed dimension
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