30 research outputs found
Phase transitions for suspension flows
This paper is devoted to study thermodynamic formalism for suspension flows
defined over countable alphabets. We are mostly interested in the regularity
properties of the pressure function. We establish conditions for the pressure
function to be real analytic or to exhibit a phase transition. We also
construct an example of a potential for which the pressure has countably many
phase transitions.Comment: Example 5.2 expanded. Typos corrected. Section 6.1 superced the note
"Thermodynamic formalism for the positive geodesic flow on the modular
surface" arXiv:1009.462
Matrix valued Brownian motion and a paper by Polya
We give a geometric description of the motion of eigenvalues of a Brownian
motion with values in some matrix spaces. In the second part we consider a
paper by Polya where he introduced a function close to the Riemann zeta
function, which satisfies Riemann hypothesis. We show that each of these two
functions can be related to Brownian motion on a symmetric space
Dévissage of a Poisson boundary under equivariance and regularity conditions
20 pages, 3 figuresWe present a method that allows, under suitable equivariance and regularity conditions, to determine the Poisson boundary of a diffusion starting from the Poisson boundary of a sub-diffusion of the original one. We then give two examples of application of this dévissage method. Namely, we first recover the classical result that the Poisson boundary of Brownian motion on a rotationally symmetric manifolds is generated by its escape angle, and we then give an "elementary" probabilistic proof of the delicate result of [Bai08], i.e. the determination of the Poisson boundary of the relativistic Brownian motion in Minkowski space-time