Dirk Erhard

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math.PR2024

Superdiffusive Scaling Limits for the Symmetric Exclusion Process with Slow Bonds

Dirk Erhard, Tertuliano Franco, Tiecheng Xu

In \cite{fgn1}, the hydrodynamic limit in the diffusive scaling of the symmetric simple exclusion process with a finite number of slow bonds of strength $n^{- β}$ has been studied.…

math.PR2024

A scaling limit of the 2D parabolic Anderson model with exclusion interaction

Dirk Erhard, Martin Hairer, Tiecheng Xu

We consider the (discrete) parabolic Anderson model $\partial u (t, x) / \partial t = Δ u (t, x) + ξ_{t} (x) u (t, x)$ , $t \geq 0$ , $x \in Z^{d}$ . Here, the $ξ$ -field is $R$ -valued,…

math.PR2023

Uniqueness and tube property for the Swiss cheese large deviations

Julien Poisat, Dirk Erhard

We consider the simple random walk on the Euclidean lattice, in three dimensions and higher, conditioned to visit fewer sites than expected, when the deviation from the mean scales…

math.PR2023

Nonequilibrium Joint Fluctuations for Current and Occupation Time in The Symmetric Exclusion Process

Dirk Erhard, Tertuliano Franco, Tiecheng Xu

We provide a full description for the joint fluctuations of current and occupation time in the one-dimensional nonequilibrium simple symmetric exclusion process, furnishing explici…