We introduce a family of models for random walks in space-time random environments, and we study the scaling limits of these models in several subcritical scaling regimes in all spatial dimensions. We show that each regime gives rise to a different limiting SPDE. These SPDEs have an effective covariance that is quite different from the covariance of the prelimiting noise. We show that at large time and space scales, there are Gaussian fluctuations up to a certain specific spatial centering radius in the tail of the quenched probability distribution of the random walk, which we call the critical scale. This critical scale depends on the spatial dimension of the underlying random walk. We conjecture that the fluctuations are no longer Gaussian at a certain point within the critical scale, which we proved in d=1 in joint works with Sayan Das. In d=2, we conjecture that the scaling limit at criticality is given by the 2d critical stochastic heat flow which was recently constructed by Caravenna, Sun, and Zygouras.
Join the Zoom meeting with the link below: https://us06web.zoom.us/webinar/register/3317636514377/WN_DZMAlup-ToWSQwgQTDvBug
Please turn off your personal videos to reduce the bandwidth used!
You can access a recording of this seminar, as well as those of past seminars, in the Youtube channel: https://www.youtube.com/@oneworldprobability3373/videos
If you are having troubles with zoom, or if the capacity of the zoom room gets exceeded, you can also access to the Youtube live stream at the channel of the seminar: https://www.youtube.com/channel/UCiLiEQGTp6bZEhuHDM-WNWQ
We use zoom, a simple webinar tool. Zoom is not free, but only the hosts (that's us) need a license. All others can log-in via a link. Before the talk you can find the link on this website. Just click on the link and you will be sent to a webinar. There will be a host with control over the microphones.
Please subscribe to our mailing list for updates about the upcoming seminars and other One World events.