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Simple random walk on the uniform infinite planar quadrangulation: subdiffusivity via pioneer points (2013).
| Content Provider | CiteSeerX |
|---|---|
| Author | Benjamini, Itai Curien, Nicolas |
| Abstract | We study the pioneer points of the simple random walk on the uniform infinite planar quadrangulation (UIPQ) using an adaptation of the peeling proce-dure of Angel (Geom Funct Anal 13:935–974, 2003) to the quadrangulation case. Our main result is that, up to polylogarithmic factors, n3 pioneer points have been discovered before the walk exits the ball of radius n in the UIPQ. As a result we verify the KPZ relation Knizhnik et al. (Modern Phys Lett A 3:819–826, 1988) in the particular case of the pioneer exponent and prove that the walk is subdiffusive with exponent less than 1/3. Along the way, new geometric controls on the UIPQ are established. |
| File Format | |
| Publisher Date | 2013-01-01 |
| Access Restriction | Open |
| Subject Keyword | Springer Basel Gafa Geometric Subdiffusivity Via Pioneer Point Pioneer Point Uniform Infinite Planar Quadrangulation New Geometric Control Simple Random Walk Main Result Polylogarithmic Factor Pioneer Exponent Modern Phys Lett Particular Case Kpz Relation Knizhnik Quadrangulation Case Geom Funct Anal |
| Content Type | Text |
