# Annealed invariance principle for random walks on random graphs generated by point processes in $\mathbb{R}^d$

@article{Rousselle2015AnnealedIP, title={Annealed invariance principle for random walks on random graphs generated by point processes in \$\mathbb\{R\}^d\$}, author={Arnaud Rousselle}, journal={arXiv: Probability}, year={2015} }

We consider simple random walks on random graphs embedded in $\mathbb{R}^d$ and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we show an annealed invariance principle for these random walks. These results hold for a large variety of point processes including Poisson point processes, Mat\'ern cluster and Mat\'ern hardcore processes which have respectively clustering and repulsiveness… Expand

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#### References

SHOWING 1-10 OF 45 REFERENCES

Recurrence or transience of random walks on random graphs generated by point processes in Rd

- Mathematics
- 2015

We consider random walks associated with conductances on Delaunay triangulations, Gabriel graphs and skeletons of Voronoi tilings generated by point processes in Rd. Under suitable assumptions on… Expand

Quenched invariance principle for random walks on Delaunay triangulations

- Mathematics
- 2014

We consider simple random walks on Delaunay triangulations generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on the point processes, we show that the random walk satisfies an… Expand

Mott Law as Upper Bound for a Random Walk in a Random Environment

- Physics, Mathematics
- 2008

We consider a random walk on the support of an ergodic simple point process on $${\mathbb{R}^d}$$, d ≥ 2, furnished with independent energy marks. The jump rates of the random walk decay… Expand

Invariance principle for Mott variable range hopping and other walks on point processes

- Mathematics, Physics
- 2013

We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the A-power of the jump length and depend on the energy marks via a… Expand

Mott Law as Lower Bound for a Random Walk in a Random Environment

- Mathematics, Physics
- 2005

We consider a random walk on the support of an ergodic stationary simple point process on ℝd, d≥2, which satisfies a mixing condition w.r.t. the translations or has a strictly positive density… Expand

Quenched invariance principle for simple random walk on percolation clusters

- Mathematics, Physics
- 2006

We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in ℤd with d≥2. We prove that, for almost every percolation configuration, the path distribution… Expand

First Passage Percolation on Random Geometric Graphs and an Application to Shortest-Path Trees

- Mathematics
- Advances in Applied Probability
- 2015

We consider Euclidean first passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic… Expand

An invariance principle for reversible Markov processes. Applications to random motions in random environments

- Physics
- 1989

We present an invariance principle for antisymmetric functions of a reversible Markov process which immediately implies convergence to Brownian motion for a wide class of random motions in random… Expand

Recurrence and transience for long range reversible random walks on a random point process

- Mathematics, Physics
- 2008

We consider reversible random walks in random environment obtained from symmetric long-range jump rates on a random point process. We prove almost sure transience and recurrence results under… Expand

Functional CLT for random walk among bounded random conductances

- Mathematics
- 2007

We consider the nearest-neighbor simple random walk on Z d , d ≥2, driven by a field of i.i.d. random nearest-neighbor conductances ω xy ∈[0,1]. Apart from the requirement that the bonds with… Expand