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12 papers · 2 filters
Superdiffusive and Subdiffusive Exceptional Times in the Dynamical Discrete Web
Dan Jenkins
The dynamical discrete web is a system of one-dimensional coalescing random walks that evolves in an extra dynamical time parameter. At any deterministic dynamical time, the paths…
Complexity of random smooth functions on the high-dimensional sphere
Antonio Auffinger, Gerard Ben Arous
We analyze the landscape of general smooth Gaussian functions on the sphere in dimension , when is large. We give an explicit formula for the asymptotic complexity of the me…
A local limit theorem for a transient chaotic walk in a frozen environment
Lasse Leskelä, Mikko Stenlund
This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the…
Limiting spectral distribution of sample autocovariance matrices
Anirban Basak, Arup Bose, Sanchayan Sen
We show that the empirical spectral distribution (ESD) of the sample autocovariance matrix (ACVM) converges as the dimension increases, when the time series is a linear process wit…
Process-Level Large Deviations for Nonlinear Hawkes Point Processes
Lingjiong Zhu
In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a r…
Einstein relation for biased random walk on Galton--Watson trees
Gerard Ben Arous, Yueyun Hu, Stefano Olla +1
We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton--Watson trees. This pr…