January 2024 CDT Mathematics of Random Systems Workshop

Student speakers: Giuseppe Tenaglia (Imperial) and Rivka Mitchell (Oxford), and Speaker talk by Dr Cris Salvi (Imperial) 

Imperial student, Guiseppe Tenaglia


14:00    Giuseppe Tenaglia (Imperial)

Topological dynamics for chaotic circle endomorphisms 

Abstract: In this talk we introduce a class of random circle endomorphism displaying positive lyapunov exponent. For such systems we propose a notion of random horseshoe and prove abundance of horseshoe-like dynamics





Oxford student, Rivka Mitchell

14:45    Rivka MacLaine Mitchell (Oxford)

Convergence of globally centered discrete snakes

Abstract: We consider branching random walks on size-conditioned critical Bienaymé-Watson trees. We show convergence of the associated discrete snakes to the Brownian snake driven by the normalized Brownian excursion. The proof relies on two different constructions of random trees. This talk is based on joint work in progress with Louigi Addario-Berry, Serte Donderwinkel, and Christina Goldschmidt


Imperial academic, Dr Cris Salvi

15:30    Speaker talk: Dr Cris Salvi (Imperial Academic) 

Scaling limits of random recurrent-residual neural networks

Abstract: I will present some scaling limit results for random recurrent and residual neural networks when width and depth tend to infinity. When the activation function is the identity, I will show that the limiting object is a Gaussian measure on some space of paths and its covariance agrees with the so-called signature kernel.