refs.bib

@book{lawler,
    title = {Random Walk: A Modern Introduction},
    author = {Gregory F. Lawler and  Vlada Limic},
    isbn = {9780511750854},
    series = { Cambridge Studies in Advanced Mathematics (123) },
    year = {2010},
    publisher = {Cambridge University Press },
    keywords = {random walk}
}

@book{evans,
    title = {Partial Differential Equations},
    author = {Lawrece C. Evans},
    series = {Graduate Studies in Mathematics},
    volume = {19},
    publisher = {American Mathamatical Society},
    year = {2010}
}

@article{lawler_idla,
    author = {Gregory F. Lawler and Maury Bramson and David Griffeath},
    title = {Internal Diffusion Limited Aggregation},
    journal = {The Annals of Probability},
    pages = "2117--2140.",
    year = "1992",
    DOI = "https://projecteuclid.org/euclid.aop/1176989542",
    keywords = "IDLA "
}

@article{jerison,
    author = {David Jerison and Lionel Levine and Scott Sheffield},
    title = {Logarithmic fluctuations for internal DLA},
    journal = { J. Amer. Math. Soc.},
    pages = "271--301",
    year = "2012",
    DOI = "https://arxiv.org/abs/1010.2483",
    keywords = "IDLA"
}

@article{levineSimulations,
    author = {T. Friedrich and L. Levine },
    title = {Fast simulation of large-scale growth models},
    booktitle="Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques",
    year="2011",
    publisher="Springer Berlin Heidelberg",
    pages="555--566",
    keywords = "simulation, growth model, IDLA"
}

@article{mccrea_whipple_1940, 
title={XXII.—Random Paths in Two and Three Dimensions}, 
volume={60}, DOI={10.1017/S0370164600020265}, 
number={3}, 
journal={Proceedings of the Royal Society of Edinburgh}, 
publisher={Royal Society of Edinburgh Scotland Foundation}, 
author={McCrea, W. H. and Whipple, F. J. W.}, 
year={1940}, 
pages={281–298}}

@article{gaudilliere,
    author = {A. Asselah and A. Gaudillière},
    title = {From logarithmic to subdiffusive polynomial fluctuations
        for internal DLA and related growth models},
    journal = {The Annals of Probability},
    pages = "1115–1159",
    year = "2013",
    DOI = "10.1214/12-AOP762",
    keywords = "IDLA, logarithimic fluctuation", 
    volume = 41
}

@article{gaudilliereSublog,
    author = {A. Asselah and A. Gaudillière},
    title = {Sublogarithmic fluctuations for internal DLA},
    journal = {The Annals of Probability},
    pages = "1160–1179",
    year = "2013",
    DOI = "doi:10.1214/11-AOP735",
    keywords = "IDLA, logarithimic fluctuation", 
    volume = 41
}

@article{Stoer,
    author = {Alfred Stoehr},
    title = {Ueber einige lineare partielle 
    Differenzengleichungen mitkonstanten Koeffizienten III},
    journal = {Math. Nachr.3},
    pages = "330--357",
    year = "1950"
}

@article{kozma,
    author = {Gady Kozma and Ehud Schreiber},
    title = {An asymptotic expansion 
    for the discrete harmonic potential},
    journal = {Electron. J. Probab.},
    pages = "1--17",
    year = "2004",
    DOI = "arXiv:math/0212156"
}

@article{meakinDeutsch,
    author = {Paul Meakin and J. M. Deutch},
    title = {The formation of surfaces by diffusionlimited annihilation},
    journal = {J. Chem. Phys.},
    pages = "2320--2325",
    year = "1986",
    volume = "85"
}

@article{lawler92,
    author = {G. F. Lawler, M. Bramson and D. Griffeath},
    title = {Internal Diffusion Limited Aggregation},
    journal = {Annals of Probability},
    pages = "2117--2140",
    year = "1992",
    volume = 20
}

@article{lawler95,
    author = {G. F. Lawler},
    title = {Subdiffusive fluctuations for internal
        diffusionlimited aggregation},
    journal = {Annals of Probability},
    pages = "71--86",
    year = "1995",
    volume = 23
}


@article{fulton,
    author = {P. Diaconis and W. Fulton},
    title = {A Growth Model, a Game, an Algebra, 
        Lagrange Inversion, and Characteristic Classes},
    journal = {Rend. Sem. Mat. Univ. Pol. Torino},
    pages = "95--119",
    year = "1991",
}

@book{revuz,
    title = {Continuous Martingales and Brownian Motion},
    author = {Daniel Revuz and Marc Yor},
    edition = {3},
    year = {1999},
    publisher = {Springer}
}

@book{spitzer, 
    title = {Principles of Random Walk},
    author = {Frank Spitzer},
    edition = {2},
    series = {Graduate Texts in Mathematics},
    year = {1976},
    publisher = {Springer}
}

@article{krugMeakinPhysics,
    author = {J. Krug and P. Meakin},
    title = {Kinetic roughening of Laplacian fronts},
    journal = {Physical Review Letters},
    pages = "703--706",
    year = "1991",
    volume = 66
}

@article{PatersonFluids,
    author = {L. Paterson},
    title = {Diffusion-Limited Aggregation and Two-Fluid 
        Displacements in Porous Media},
    journal = {Physical Review Letters},
    pages = "1621--1624",
    year = "1984",
    volume = 52
}

@article{ChaoTangFluids,
    author = {C. Tang},
    title = {Diffusion-limited aggregation and the Saffman-Taylor problem},
    journal = {Physical Review},
    pages = "1977--1979",
    year = "1977",
    volume = 31,
    DOI =  "10.1103/PhysRevA.31.1977"
}

@article{HussChomb,
    author = {W. Huss and E. Sava},
    title = {Internal Aggregation Models on Comb Lattices},
    journal = {Electronic Journal of Probability},
    pages = "1--21",
    year = "2012",
    volume =  17,
    DOI =  "arXiv:1106.4468v2"
}

@article{CandelleroWater,
    author = {E. Candellero and S. Ganguly and C. Hoffman and L. Levine},
    title = {Oil and water: A two-type internal aggregation model},
    journal = {Electronic Journal of Probability},
    pages = "4019-4070",
    year = "2017",
    volume =  45,
    DOI =  "doi:10.1214/16-AOP1157"
}

@article{JLScylinders,
    author = {D. Jerison and L. Levine and S. Sheffield},
    title = {Internal DLA for cylinders},
    journal = {Advances in Analysis: The Legacy of Elias M. Stein},
    pages = "189-213",
    year = "2014",
    publisher =  "Princton University Press"
}

@article{percolationClusters,
    author = {Eric Shellef},
    title = {IDLA on the Supercritical Percolation Cluster},
    journal = {Electron. J. Probab.},
    pages = "723-740",
    volume = 15,
    year = "2010",
}

@misc{asselah2011lower,
    title={Lower bounds on fluctuations for internal DLA},
    author={Amine Asselah and Alexandre Gaudilliere},
    year={2011},
    eprint={1111.4233},
    archivePrefix={arXiv},
    primaryClass={math.PR}
}