TY - JOUR

T1 - On the volume of tubular neighborhoods of real algebraic varieties

AU - Lotz, Martin

PY - 2014/12/23

Y1 - 2014/12/23

N2 - 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 The bounds are given in terms of the degrees of the defining polynomials, and contain as a special case an unpublished result by Ocneanu.

AB - 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 The bounds are given in terms of the degrees of the defining polynomials, and contain as a special case an unpublished result by Ocneanu.

U2 - 10.1090/S0002-9939-2014-12397-5#sthash.uZeTJlDV.dpuf

DO - 10.1090/S0002-9939-2014-12397-5#sthash.uZeTJlDV.dpuf

M3 - Article

SN - 0002-9939

JO - American Mathematical Society. Proceedings

JF - American Mathematical Society. Proceedings

ER -