## 2012.87: On the volume of tubular neighborhoods of real algebraic varieties

2012.87:
Martin Lotz
(2012)
*On the volume of tubular neighborhoods of real algebraic varieties.*

*This is the latest version of this eprint.*

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## Abstract

The problem of determining the volume of a tubular neighbourhood has a long and rich history. Bounds on the volume of neighbourhoods of algebraic sets have turned out to play an important role in the probabilistic analysis of condition numbers in numerical analysis. We present a self-contained derivation of bounds on the probability that a random point, chosen uniformly from a ball, lies within a given distance of a real algebraic variety of any codimension. The bounds are given in terms of the degrees of the defining polynomials, and contain as special case an unpublished result by Ocneanu.

Item Type: | MIMS Preprint |
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Subjects: | MSC 2000 > 51 Geometry (See also algebraic geometry) MSC 2000 > 53 Differential geometry MSC 2000 > 60 Probability theory and stochastic processes MSC 2000 > 65 Numerical analysis |

MIMS number: | 2012.87 |

Deposited By: | Dr. Martin Lotz |

Deposited On: | 11 October 2013 |

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- On the volume of tubular neighborhoods of real algebraic varieties (deposited 11 October 2013)
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