P.B'erard, G.Besson and A.S.Gallot, Sur une in'egalit'e isop'erim'etrique qui g'eneralise celle de Paul Levy - Gromov, Inventiones Mathematicae 80 (1985)295-308. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Computing The Volume Of Convex Bodies: A Case Where Randomness .. - Dyer, Frieze (1991) (23 citations) (Correct)
....made precise later. The algorithm itself is a fairly simple random walk. The difficulties lie in the analysis. The analysis of [10] used the idea of rapidly mixing Markov chains , and exploited a powerful isoperimetric inequality on the boundary of convex sets due to B erard, Besson and Gallot [5] in order to prove a crucial property of the random walk. A different isoperimetric inequality was also conjectured in [10] concerning the exposed surface area of volumes in the interior of convex sets, which would improve the time bound of the algorithm. Aldous and Diaconis (see, for ....
....for example, in [15] Intuitively, conductance is a measure of probability flow in the chain. More formally, it measures the isoperimetry of a natural weighted digraph underlying the chain. Good conductance implies rapid mixing. It was precisely to prove good conductance that the inequality of [5] was required in [10] Recently, Lov asz and Simonovits [24] generalized the notion of conductance, and gave a sharper proof that this implies rapid mixing (although in a weaker sense than Sinclair and Jerrum [30] They also proved the above conjecture of [10] See also Karzanov and Khachiyan ....
P. B'erard, G. Besson and A. S. Gallot, Sur une in'egalit'e isop'erim'etrique qui g'eneralise celle de Paul LevyGromov, Inventiones Mathematicae 80 (1985), 295--308.
A Random Polynomial Time Algorithm For Approximating The.. - Dyer, Frieze, Kannan (1995) (79 citations) (Correct)
No context found.
P.B'erard, G.Besson and A.S.Gallot, Sur une in'egalit'e isop'erim'etrique qui g'eneralise celle de Paul Levy - Gromov, Inventiones Mathematicae 80 (1985)295-308.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC