On the volume of tubular neighborhoods of real algebraic varieties
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- by Martin Lotz PDF
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Abstract:
The problem of determining the volume of a tubular neighborhood has a long and rich history. Bounds on the volume of neighborhoods 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 The bounds are given in terms of the degrees of the defining polynomials, and contain as a special case an unpublished result by Ocneanu.References
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Additional Information
- Martin Lotz
- Affiliation: School of Mathematics, The University of Manchester, Alan Turing Building, Oxford Road, Manchester, M139PL, United Kingdom
- Email: martin.lotz@manchester.ac.uk
- Received by editor(s): April 2, 2013
- Received by editor(s) in revised form: September 20, 2013, and September 24, 2013
- Published electronically: December 23, 2014
- Additional Notes: This research was supported by Leverhulme Trust grant R41617 and a Seggie Brown Fellowship of the University of Edinburgh
- Communicated by: Daniel Ruberman
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 1875-1889
- MSC (2010): Primary 14P05, 53C65; Secondary 60D05, 15A12
- DOI: https://doi.org/10.1090/S0002-9939-2014-12397-5
- MathSciNet review: 3314098