We establish a large deviation principle for chordal SLE\(_\kappa\) parametrized by capacity, as the parameter \(\kappa \to 0+\), in topology generated uniform convergence on compact intervals of positive real line. The rate function is shown to equal Loewner energy curve. This strengthens recent result Peltola and Wang who obtained analogous statement using Hausdorff topology.

A simple proof of Donsker-Varadhan’s large deviation principle (LDP) for occupation measure of Markov process, valued in R, with the discrete time is given. A proof is based on a new version of Dupui-Ellis’s large deviation principle for two-dimensional occupation measures. In our setting, an existence of the invariant measure does not assumed. This condition is replaced (from point of view of ...

In this paper we establish the large deviation principle for two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both small noise and short time. The proof is based on weak convergence approach. For time asymptotics use exponential equivalence to prove result.

The present work is concerned with two-dimensional stochastic subcritical and critical convective Brinkman-Forchheimer (2 D SCBF) equations perturbed by a white noise (non-degenerate) in smooth bounded domains R2. We establish two important properties of the Markov semigroup associated solutions 2 SCBF (for absorption exponent r = 1, 2, 3), that is, irreducibility strong Feller property. These ...

Conditioning a branching Brownian motion to have an atypically low maximum leads suppression of the mechanism. In this note, we consider conditioned below $\sqrt{2}\alpha t$ ($\alpha<1$). We study precise effects early/late first time and low/high location under condition. do so by imposing additional constraints on location. obtain large deviation estimates, as well optimal given constraints.