We prove a large deviation principle for additive functionals of local Lipschitz functions of a one-dimensional symmetric zero-range process on the diffusive scale. The rate function is obtained from the dynamical large deviation principle for the empirical density and is characterized by a variational constraint involving the density at a fixed spatial point. On the microscopic side, a super-exponential replacement is needed to replace the local observable with a function of the empirical density. On the macroscopic side, the spatial regularity enjoyed by finite-rate trajectories is needed to pass from spatial averages to point evaluation.
For a large class of discrete- and continuous-time models satisfying a linear flow property, we prove convergence to the critical $2d$ stochastic heat flow under diffusive scaling of space and time. Convergence is in the sense of finite-dimensional distributions in the space of measure-valued stochastic flows. The clas...
Hindy Drillick, Jonathan Hou, Shalin Parekh· 0 citations
We study a Brownian particle in $\mathbb{R}^d$, $d\geq2$, with drift given by the gradient of a log-correlated Gaussian potential. At weak disorder, we prove convergence to a scaling limit whose law is singular with respect to Brownian motion and whose invariant measure is given by Gaussian multiplicative chaos. The pr...
Scott Armstrong, Ahmed Bou-Rabee, Tuomo Kuusi· 0 citations
We establish level-1 large deviation principles for continuous time suspension flows over countable Markov shifts, a class of non compact dynamical systems. Our results both quantify deviations of Birkhoff averages from their typical values and, importantly, provide a large deviation principle for orbits that at a fini...
Godofredo Iommi, Thomas Jordan, Anibal Velozo· 0 citations
We study a one-dimensional self-consistent transfer operator generated by a repulsive mean-field coupling. The interaction admits a natural interpretation as a myopic relocation dynamics balancing congestion and uniformly distributed resources. Using the quantile representation of probability measures, combined with se...
Roberto Castorrini, S. Galatolo, Matteo Tanzi· 0 citations
This work is a step towards a general understanding of fluctuations for systems of particles described at large scale by fractional diffusion. First, we derive formally a Large Deviation Principle for the empirical measure of mean-field interacting particles with a L{\'e}vy-type noise. In the case of independent partic...
We prove moderate deviation principles and laws of the iterated logarithm in the sparse regime for geometric and topological functionals associated with $k$-point connected components. These limit theorems are established at both the measure-valued and vector-valued levels, for Poisson and binomial point processes. As...
Yudai Sakihara, K. Tsunoda· 0 citations
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