University of Cambridge > > Probability > From disorder relevance to the 2d Stochastic Heat Equation.

From disorder relevance to the 2d Stochastic Heat Equation.

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Perla Sousi.

We consider statistical mechanics models defined on a lattice, such as pinning models, directed polymers, random field Ising model, in which disorder acts as an external random field. Such models are called disorder relevant, if arbitrar- ily weak disorder changes the qualitative properties of the model. Via a Lindeberg principle for multilinear polynomials we show that disorder relevance manifests it- self through the existence of a disordered high-temperature limit for the partition function, which is given in terms of Wiener chaos and is model specific. When disorder becomes marginally relevant a fundamentally new structure emerges, which leads to a universal scaling limit for all different (currently of directed poly- mer type) models that fall in this class. A notable such representative is the two dimensional SHE with multipicative space-time white noise (which in the SPDE language is characterised as “critical”). In this case certain analogies with Gaussian Multiplicative Chaos and log-correlated Gaussian fields appear. Based on joint works with Francesco Caravenna and Rongfeng Sun.

This talk is part of the Probability series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2023, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity