Probability Seminar

Organisers

Giuseppe CannizzaroLink opens in a new window and Nikolaos ZygourasLink opens in a new window

The probability seminar is held on Wednesdays 16-17 in B3.02.

Seminars in Term 1.

Oct 8 - Christophoros Panagiotis (University of Bath)

Title: Geometric representations for the $\varphi^4$ model

Abstract: The $\varphi^4$ model was originally introduced in Quantum Field Theory as the simplest candidate for a non-Gaussian theory. Its importance in statistical physics was highlighted by Griffiths and Simon, who observed that the $\varphi^4$ potential arises as the scaling limit of the fluctuations of the critical Ising model on the complete graph. In this talk, I will describe how this connection to the Ising model leads to two new geometric representations of the $\varphi^4$ model, called the random tangled current expansion and the random cluster model. I will explain how these representations can be used to prove that the phase transition of the $\varphi^4$ model is continuous in dimensions three and higher, and to obtain large-deviation estimates for spin averages in the supercritical regime.

Oct 15 - Omer Angel and Daniel de la Riva Massaad (University of British Columbia)

Title: The phase transitions in the frog model.

Abstract: The frog model is an interacting particle system, where particles are of type A (asleep) until hit by a particle of type B. Despite the simplicity of the definition, many questions remain open. We prove existence and sharpness of the phase transition for the frog model on transitive graphs of either polynomial growth, or non-amenable.

Oct 22 - Jad Hadman (University of Oxford)

Title: Log-correlated fields, Gaussian mutiplicative chaos and the Riemann zeta function

Abstract: In a pair of highly influential works, Fyodorov, Hiary and Keating formulated precise conjectures on the extreme value statistics of the Riemann zeta function on typical short intervals of the critical line Re(z)=1/2. These conjectures have since seen substantial progress, and have more generally stimulated work connecting multiplicative number theory with the study of log-correlated fields and Gaussian multiplicative chaos. In this talk, I will explore these connections and present recent results that advance this program. (Based on joint work with L-P. Arguin.)

Oct 29 -

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Nov 5 - SPECIAL OPEN PROBLEM SESSION with Bálint Tóth

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Nov 12 - Thierry Bodineau (Institut des Hautes Études Scientifique)

Title: A renormalisation group perspective on functional inequalities

Abstract: Functional inequalities provide information on the structure of a probability measure and on the relaxation of associated stochastic dynamics to equilibrium. In this talk, we will describe a multiscale analysis for decomposing high-dimensional measures into simpler structures and derive from it functional inequalities. The strategy is based on the renormalization group method used in statistical physics to study the distribution of interacting particle systems. We will also review other related developments and in particular show that this decomposition of measures can be interpreted in terms of measure transport.

Nov 19 - Darrick Lee (University of Edinburgh)

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Nov 26 - Quentin Berger (Université Sorbonne Paris Nord)

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Dec 3 -

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Dec 10 - Matt Roberts (University of Bath)

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