7 problems

Consider the deterministic two-dimensional viscous incompressible fluid–structure system in which a perfectly elastic shell is governed by a linearised beam equation and forms the…

Let $X$ solve a multidimensional stochastic differential equation driven by fractional Brownian motion, with initial condition $X_0=x_0$, and suppose that the system is uniformly e…

For deep residual networks whose weights are initialized with correlations across layers, the infinite-depth limiting dynamics should interpolate continuously between the stochasti…

Let $(\mathcal{M},g)$ be a Riemannian manifold, let $A$ be a smooth vector field, and let $\mu$ be the loop measure determined by the diffusion with generator … Assume that the dif…

Let $W$ be the Brownian motion and let $G$ be the Green kernel appearing in the definition of the renormalised Amperean area. Write $I_W$ for the recentred self-intersection local…

Invariant-property conjecture. For any pair $(\gamma,\rho)$, there exists a property $\mathcal{P}$ such that:

Let $\mathcal{B}$ be the stochastic Bessel operator, let $f\in L^2[0,1]$, and let $X$ be the stochastic process formally satisfying … with functional … Let $A$ be the event…