Andrea Clini (Oxford)
Particle Systems & Stochastic PDEs: analysis of models in fluctuating hydrodynamics and neuroscience abstract
Abstract:
In this presentation I give an overview of my research area, and discuss my accomplishments and future directions of investigation. My work so far has investigated the interplay between PDEs and particle systems through the study of two classes of models. The first class is the so-called generalized Dean-Kawasaki equation coming from areas like fluctuating hydrodynamics, mean-field theory and stochastic geometry. The second class is a generalized model for interacting neurons encompassing many of those commonly used in computational neuroscience, in particular in the study of grid cells. For the first model I focus more on the PDE side, while for the second I concentrate on the particle side, where I have given my contributions, respectively. For both models I also present aspects of current and future investigation. Finally, I will discuss other research directions to be pursued in the coming period.
09:00 • EPF Lausanne, Bernoulli Center
Lukasz Madry (Paris-Dauphine)
Regularisation by fractional noise and the zero noise limit abstract
Abstract:
In the talk, I will present the results from my thesis on the limit of zero noise for the singular SDEs driven by the fractional Brownian motion. I will present the proof of convergence towards the extremal solutions in the Peano example in the full Catellier-Gubinelli regime (which is to say we can consider arbitrarily singular power-law function), along with the upper bound for the convergence rate. The proof uses techniques from regularisation by noise and the study of ergodicity of fractional SDEs, established by Hairer and Panloup-Richard. Time permitting, I will discuss ongoing work on the multidimensional case and remaining open problems, along with some possible ideas on how to solve them.
10:00 • EPF Lausanne, Bernoulli Center
Sotiris Kotitsas (Warwick)
Regularisation by fractional noise and the zero noise limit abstract
Abstract:
We consider the stochastic heat equationand the related KPZ equationin the critical dimension d = 2 where V is a Gaussian random potential and β is the noise strength. We will focus on the case where the potential is not white in time and study the large-scale fluctuations of u(t, x) and h(t, x). We show that after renormalizing, the fluctuations converge to the Edwards-Wilkinson limit with an explicit effective variance and constant effective diffusivity. We discuss our main tools, a specific Markov chain on the space of paths and an extension of the Kallianpur-Robbins law to a specific regenerative process. Time permitting, we will also discuss possible future directions.
11:00 • EPF Lausanne, Bernoulli Center
Heather Battey (Imperial College, London)
Maximal co-ancillarity and maximal co-sufficiency abstract
Abstract:
This will be an expository talk, rather than a research talk. The purpose is to provide some alternative perspectives on conditional inference through a notional idealised separation within the minimal sufficient statistic, allowing a geometric account of key ideas from the Fisherian position on conditional inference. The notional idealised separation, in terms an ancillary statistic and what I call a maximal co-ancillary statistic, provides insight and clarifies what is sought from an approximate conditional analysis, where exact calculations may not be available.A parallel framework applies in the Fisherian assessment of model adequacy.Both aspects will be discussed and illustrated geometrically through examples.
15:15 • EPF Lausanne, CM 1 517