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math.PR 1

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2024 1

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CONDITIONAL 1

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Approximately Jumping Towards the Origin

math.PR · 2024-12-05 · conditional · novelty 7.0

For i.i.d. uniform random directions on the sphere, the greedy sign choice has a unique invariant radial measure with mean sqrt(pi)/2 * Gamma((d+1)/2)/Gamma(d/2) ~ sqrt(pi d/8).

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  • Approximately Jumping Towards the Origin math.PR · 2024-12-05 · conditional · none · ref 6

    For i.i.d. uniform random directions on the sphere, the greedy sign choice has a unique invariant radial measure with mean sqrt(pi)/2 * Gamma((d+1)/2)/Gamma(d/2) ~ sqrt(pi d/8).