5 papers · 1 filter
The continuum parabolic Anderson model with a half-Laplacian and periodic noise
Alexander Dunlap
We construct solutions of a renormalized continuum fractional parabolic Anderson model, formally given by , where is a periodic spatial white nois…
Tightness of Liouville first passage percolation for
Jian Ding, Julien Dubédat, Alexander Dunlap +1
We study Liouville first passage percolation metrics associated to a Gaussian free field mollified by the two-dimensional heat kernel in the bulk, and related star-scale…
Subsequential scaling limits for Liouville graph distance
Jian Ding, Alexander Dunlap
For and , we consider the Liouville graph distance, which is the minimal number of Euclidean balls of -Liouville quantum gravity measure at most whose union con…
Fluctuations of the solutions to the KPZ equation in dimensions three and higher
Alexander Dunlap, Yu Gu, Lenya Ryzhik +1
We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in with a small coupling constant, driven…
Constructing a solution of the -dimensional KPZ equation
Sourav Chatterjee, Alexander Dunlap
The -dimensional KPZ equation is the canonical model for the growth of rough -dimensional random surfaces. A deep mathematical understanding of the KPZ equation for …