B. Hambly

Variance-Feedback Noise in Interacting Diffusions: Shape Dynamics and Mean-Field Limits

We study a system of $N$ attractive interacting diffusions where the variance feeds back into the noise. That is the common and idiosyncratic Brownian forcing has amplitude $\kappa(S_t^N)^q$, with $S_t^N$ the empirical variance of the system, $\kappa>0$ and $q\geq 0$. With the interaction kernel given by $K(z)=|z|^p z$...