# Strongly mixing smooth planar vector field without asymptotic directions

@inproceedings{Bakhtin2019StronglyMS, title={Strongly mixing smooth planar vector field without asymptotic directions}, author={Yuri Bakhtin and Liying Li}, year={2019} }

. We use a Voronoi-type tesselation based on a compound Poisson point process to construct a polynomially mixing stationary random smooth planar vector ﬁeld with bounded nonnegative components such that, with probability one, none of the associated integral curves possess an asymptotic direction.

## References

SHOWING 1-10 OF 18 REFERENCES

### Weakly mixing smooth planar vector field without asymptotic directions

- Mathematics
- 2018

We construct a planar smooth weakly mixing stationary random vector field with nonnegative components such that, with probability 1, the flow generated by this vector field does not have an…

### Geodesics in two-dimensional first-passage percolation

- Mathematics
- 1996

We consider standard first-passage percolation on Z 2 . Geodesics are nearest-neighbor paths in Z 2 , each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite…

### Asymptotic Behaviour of Semi-Infinite Geodesics for Maximal Increasing Subsequences in the Plane

- Mathematics
- 2002

We consider for a given Poissonian cloud ω in ℝ2the maximal up/right path fromxto y(x, y∈ ℝ2), where maximal means that it contains as many points ofω as possible. We prove that with probability 1…

### Asymptotic shapes for stationary first passage percolation

- Mathematics
- 1995

This paper deals with first passage percolation where the usual i.i.d. condition is weakened to stationarity (and ergodicity). The well known asymptotic shape result is known to extend to this case.…

### A shape theorem and semi-infinite geodesics for the Hammersley model with random weights

- Mathematics
- 2010

In this paper we will prove a shape theorem for the last passage percolation model on a two dimensional $F$-compound Poisson process, called the Hammersley model with random weights. We will also…

### Stationary random walks on the lattice

- Mathematics
- 2016

We consider translation invariant measures on configurations of nearest-neighbor arrows on the integer lattice. Following the arrows from each point on the lattice produces a family of semi-infinite…

### Stochastic Homogenization of Nonconvex Hamilton‐Jacobi Equations: A Counterexample

- Mathematics
- 2015

This paper provides a counterexample to Hamilton‐Jacobi homogenization in the nonconvex case for general stationary ergodic environments.© 2016 Wiley Periodicals, Inc.

### Shortest spanning trees and a counterexample for random walks in random environments

- Mathematics
- 2005

We construct forests that span ℤd, d≥2, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For d≥3, two…

### Homogenization for¶Stochastic Hamilton-Jacobi Equations

- Mathematics
- 2000

Abstract:Homogenization asks whether average behavior can be discerned from partial differential equations that are subject to high-frequency fluctuations when those fluctuations result from a…

### Stochastic homogenization of Hamilton–Jacobi equations and some applications

- Mathematics
- 1999

Homogenization-type results for the Cauchy problem for first-order PDE (Hamilton-Jacobi equations) are presented. The main assumption is that the Hamiltonian is superlinear and convex with respect to…