arXiv subjects

Tim Ferguson

Publications and source records attributed to Tim Ferguson.

2 recordsLinked to original sources

arXiv2017

Stable Configurations in Social Networks

We present and analyze a model of opinion formation on an arbitrary network whose dynamics comes from a global energy function. We study the global and local minimizers of this energy, which we call stable opinion configurations, and describe the global minimizers under certain assumptions on the friendship graph. We show a surprising result that the number of stable configurations is not necessarily monotone in the strength of connection in the social network, i.e. the model sometimes supports more stable configurations when the interpersonal connections are made stronger.

math.DS↗

arXiv2017

$H^\infty$-calculus for semigroup generators on BMO

We prove that the negative infinitesimal generator $L$ of a semigroup of positive contractions on $L^\infty$ has a bounded $H^\infty(S_\eta^0)$-calculus on the associated Poisson semigroup-BMO space for any angle $\eta>\pi/2$, provided the semigroup satisfies Bakry-Emry's $\Gamma_2 $ criterion. Our arguments only rely on the properties of the underlying semigroup and works well in the noncommutative setting. A key ingredient of our argument is a quasi monotone property for the subordinated semigroup $T_{t,\alpha}=e^{-tL^\alpha},0<\alpha<1$, that is proved in the first half of the article.

math.FA↗