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2012.87: On the volume of tubular neighbourhoods of real algebraic varieties

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

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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 The bounds are given in terms of the degrees of the defining polynomials, and contain as special case an unpublished result by Ocneanu.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
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:16 October 2012

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