Stochastic bridges: From Avon to Arno 

• Ziyang Liu, University of Warwick: Moments of the Stochastic Heat Flow.
  The Critical 2d Stochastic Heat Flow (SHF) is a stochastic process on random measures on R2 that describes a non-trivial solution to the two-dimensional stochastic heat equation with multiplicative space-time noise. Its one-time marginals are a.s. singular with respect to the Lebesgue measure, meaning that the volume they assign on shrinking balls decays to zero faster than their Lebesgue volume. In this work we explore the intermittency properties of the Critical 2d SHF by studying the asymptotics of the h-th moment of the volume that it assigns on shrinking balls of radius ε and we determine that its ratio to the Lebesgue volume is of order (log 1/ε)^{h\choose 2} up to possible lower order corrections.

• Harry Giles, University of Warwick: Diffusivity of Glauber dynamics for dimers.
  In this talk, I will introduce a model of discrete surface growth in 2+1 dimensions. Naturally, one would like to determine the rate at which correlations spread through the system. We can show that they spread diffusively, which leads one to conjecture that the model lies in the Edwards-Wilkinson class. 

•  Sotirios Kotitsas, University of Pisa: On the correction to the quenched CLT of a diffusion in a space-time random environment
  We consider a diffusion in a Gaussian random environment that is white in time, and we are interested in the large-scale behavior of the quenched density with respect to the Lebesgue measure.  In $d=1$, we will discuss known results about the model, and how it can be connected to the KPZ equation, and in $d\geq2$, we will discuss the model's relevance to the statistical theory of turbulence. Finally, we will present ongoing work with Mario Maurelli and Dejun Luo about the fluctuations around the quenched local central limit theorem.

•  Lukas Gräfner, University of Warwick: Energy solutions and critical singular SPDEs

In this talk I will mainly focus on two models: First, we will discuss stochastic quasigeostrophic equations, driven by the spatial derivative of space-time white noise in d=2. We show weak-wellposedness of energy solutions and derive further properties such as non-Gaussianity and scaling-invariance. Second, we consider a singular SDE with distribution-valued, path-dependent drift that can be analysed via its 'environment-process', a certain infinite-dimensional auxiliary object that turns out to solve an SPDE which fits into our framework for energy solutions. Based on joint works with Harry Giles, Nicolas Perkowski and Shyam Popat.

• Silvia Morlacchi, University of Pisa: Two-point motion in time-correlated stochastic velocity field

We numerically investigate the two-point motion of tracer particles advected by a time-correlated stochastic velocity field, a synthetic model for turbulence. The single particle motion and the two-point motion are influenced by different phenomena. The one-point motion is driven by sweeping effects: velocity field fluctuations on the largest scale of the system. The two-point motion, in contrast, is driven by fluctuations on scales of the order of inter-particle distance. In the case of a time delta-correlated stochastic field (Kraichnan model) the splitting phenomenon occurs: tracer particles having the same initial position separate in finite time. We investigate the time-correlated case, to understand if the splitting phenomenon still occurs. Based on ongoing work with Mario Maurelli.

• Maria Chiara Ricciuti, Imperial College: Scaling Limits of Weakly-Perturbed Corner Flip Dynamics
  In this talk, we consider a random interface model on the one-dimensional discrete torus of size $2n$. The dynamics are those of corner flips with a weak perturbation, namely an asymmetry of order $n^{-\gamma}$ of the direction of growth that switches from up to down based on the sign of the area underneath. The evolution of the interface can be studied in terms of the density field of an underlying exclusion process. We show that, for $\gamma=1$, the hydrodynamic equation of the empirical measure is given by a time concatenation of the viscous Burgers' equation and the heat equation, and for $\gamma>\frac{6}{7}$ we establish convergence in law of the equilibrium fluctuations to an infinite-dimensional Ornstein-Uhlenbeck process. Based on joint work with Patrícia Gonçalves and Martin Hairer.

• Sarah-Jean Meyer, Oxford University: Characterisations of the sine-Gordon QFT

I will give a brief introduction to a forward backward SDE (FBSDE) approach to stochastic quantization. In the case of the sine-Gordon quantum field theory in the first few regions, this FBSDE is a stable description of the infinite volume measure which allows to derive a number of properties (such as Osterwalder Schrader axioms, a large deviations principle and decay of correlations). Finally, I will present some ongoing work on characterizations of the sine-Gordon QFT using a martingale problem and an integration by parts formula.

• Federico Butori, Scuola Normale Superiore: On a class of scaling limits for the stochastic vector advection equation with applications to Magnetohydrodynamics

I will present a class of scaling limits, motivated by turbulent advection in fluids, that were introduced by Galeati (Stoch. PDE: Anal Comp 8, 2020) for a stochastic transport equation. I will deal with the vector analogous of the transport equation, the Induction Equations for a magnetic field in a conducting fluid. For these equations, the presence of vector-stretching, makes the original argument by Galeati apparently inapplicable, since the stretching becomes incontrollable in the scaling argument. I will show how to (partially) circumvent this problem and I will show how from the scaling argument it is possible to rigorously derive some mean-field MHD equations, that were formally derived in the ‘60s by Steenbeck, Krause and R\"adler.