One-dimensional scaling limits in a planar Laplacian random growth model

J. Norris, V. Silvestri, and A. Turner, Scaling limits for planar aggregation with subcritical fluctuations, preprint available at https://arxiv.org/abs/1902.01376

Original

1902

Earlier work this paper cites.

M. Eden, A two-dimensional growth process, 1961 Proc. 4th Berkeley Sympos. Math. Statist. and Prob. IV

1961

Earlier work this paper cites.

D.A. Freedman, On tail probabilities for martingales, Ann. Probab. 3

1975

Earlier work this paper cites.

T.A. Witten, Jr., L.M. Sander, Diffusion-limited aggregation: a kinetic critical phenomenon, Phys. Rev. Lett. 47

1981

Earlier work this paper cites.

L. Niemeyer, L. Pietronero, and H.J. Wiesmann, Fractal dimension of dielectric breakdown, Phys. Rev. Lett. 52

1984

Earlier work this paper cites.

H. Kesten, Hitting probabilities of random walks on ℤ d \mathbb{Z}^{d} , Stochastic Processes Appl. 25

1987

Earlier work this paper cites.

Ch. Pommerenke, Boundary behaviour of conformal maps, Springer-Verlag, Berlin-Heidelberg, 1992

1992

Earlier work this paper cites.

M.B. Hastings and L.S. Levitov, Laplacian growth as one-dimensional turbulence, Phys. D 116

1998

Earlier work this paper cites.

B. Davidovitch, H.G.E. Hentschel, Z. Olami, I. Procaccia, L.M. Sander, and E. Somfai, Diffusion limited aggregation and iterated conformal maps, Phys. Rev. E 87

1999

Earlier work this paper cites.

N.G. Makarov, Fine structure of harmonic measure, St Petersburg Math. J. 10

1999

Cited alongside, same era.

L. Carleson and N. Makarov, Aggregation in the plane and Loewner’s equation, Comm. Math. Phys. 216

2001

Cited alongside, same era.

M.B. Hastings, Growth exponents for 3.99 3.99 walkers, Phys. Rev. E 64

2001

Cited alongside, same era.

L. Carleson and N. Makarov, Laplacian path models. Dedicated to the memory of Thomas H. Wolff, J. Anal. Math. 87

2002

Cited alongside, same era.

J. Mathiesen and M.H. Jensen, Tip splittings and phase transition in the dielectric breakdown model: mapping to the diffusion-limited aggregation model, Phys. Rev. Lett. 88

2002

Cited alongside, same era.

G.F. Lawler, Conformally invariant processes in the plane, Math. Surveys and Monogr. 114

F. Johansson and A. Sola, Rescaled Lévy-Loewner hulls and random growth, Bull. Sci. Math. 133

2009

Later among the works it cites.

F. Johansson Viklund, A. Sola, and A. Turner, Scaling limits of anisotropic Hastings-Levitov clusters, Ann. Inst. Henri Poincaré Probab. Stat. 48

2012

Later among the works it cites.

J. Norris and A. Turner, Hastings-Levitov aggregation in the small-particle limit, Comm. Math. Phys. 316

2012

Later among the works it cites.

F. Johansson Viklund, S. Rohde, and C. Wong, On the continuity of SLE ⁡ ( κ ) \mathrm{SLE}(\kappa) in κ \kappa , Probab. Theory Related Fields 159

2014

Later among the works it cites.

F. Johansson Viklund, Convergence rates for loop-erased random walk and other Loewner curves, Ann. Probab. 43

2015

Later among the works it cites.