![]() |
COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. | ![]() |
University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Invariant measures of the infinite Atlas model: domains of attraction, extremality, and equilibrium fluctuations
![]() Invariant measures of the infinite Atlas model: domains of attraction, extremality, and equilibrium fluctuationsAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact nobody. SSD - Stochastic systems for anomalous diffusion The infinite Atlas model describes a countable system of competing Brownian particles where the lowest particle gets a unit upward drift and the rest evolve as standard Brownian motions. The stochastic process of gaps between the particles in the infinite Atlas model has a one parameter family {p(a), a > 0} of product form mutually singular stationary distributions. We say that an initial distribution of gaps is in the weak domain of attraction of the stationary measure p(a) if the time averaged laws of the stochastic process of the gaps, when initialized using that distribution, converge to p(a) weakly in the large time limit. We provide general sufficient conditions on the initial gap distribution of the Atlas particles for it to lie in the weak domain of attraction of p(a) for each a. Results on extremality and ergodicity of p(a) will be presented. Finally, time permitting, we will describe some recent results on fluctuations of the Atlas model from inhomogeneous stationary profiles. This is based on joint work with Sayan Banerjee and Peter Rudzis. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:
Note that ex-directory lists are not shown. |
Other listsEconomics and Philosophy Carbon Nanotube Optimization and Incentives SeminarOther talksTBA The Transition to Agriculture at the edges of Eurasia ~ Neolithisation in the British Isles and the Jomon-Yayoi transition ~ Constructing Anomalous Stochastic Models of Sea Turtle Foraging, Cell Migration and Bumblebee Flights from Experimental Data Director's Welcome and Organiser's Introduction To infinity and beyond! Numerical linear algebra in infinite dimensions Quadratic spectral concentration of characteristic functions |