an:06075448
Zbl 1278.60144
Liggett, Thomas M.; Vandenberg-Rodes, Alexander
Stability on \(\{0, 1, 2, \dots \}^{S}\): birth-death chains and particle systems
EN
Br??nd??n, Petter (ed.) et al., Notions of positivity and the geometry of polynomials. Dedicated to the memory of Julius Borcea. Basel: Birkh??user (ISBN 978-3-0348-0141-6/hbk; 978-3-0348-0142-3/ebook). Trends in Mathematics, 311-329 (2011).
2011
a
60K35 33C45 60G50 60J80 62H20
stable polynomials; birth-death chain; negative association; reaction-diffusion processes
Authors' abstract: A strong negative dependence property for measures on \(\{0,1\}^n\)-stability was recently developed in [\textit{J. Borcea} et al., J. Am. Math. Soc. 22, No. 2, 521--567 (2009; Zbl 1206.62096)], by considering the zero set of the probability generating function. We extend this property to the more general setting of reaction-diffusion processes and collections of independent Markov chains. In one dimension the generalized stability property is now independently interesting, and we characterize the birth-death chains preserving it.
For the entire collection see [Zbl 1222.00033].
Mihai Gradinaru (Rennes)
Zbl 1206.62096