On the volume of tubular neighbourhoods of real algebraic varieties

Lotz, Martin (2012) On the volume of tubular neighbourhoods of real algebraic varieties. [MIMS Preprint]

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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 The bounds are given in terms of the degrees of the defining polynomials, and contain as special case an unpublished result by Ocneanu.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 2010, the AMS's Mathematics Subject Classification > 51 Geometry (See also algebraic geometry) MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Dr. Martin Lotz
Date Deposited:	16 Oct 2012
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1881

Available Versions of this Item

• On the volume of tubular neighbourhoods of real algebraic varieties. (deposited 16 Oct 2012) [Currently Displayed]
  • On the volume of tubular neighborhoods of real algebraic varieties. (deposited 11 Oct 2013)

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