Literature
Competing first passage percolation on Zd
The model was introduced in [15], where it was also shown that two types with equal
intensity can coexist in d = 2. This is generalized to higher dimensions (and more general
passage time distributions) independently in [13] and [17]. Partial results concerning
non-coexistence are proved in [16, 14] and the full coexistence conjecture is proved in thehalf-plane in [3]. Further references can be found in the survey [8].
Competing first passage percolation on the configuration model
Exponential passage times are treated in [10] (power law with finite mean but infinitevariance), [4] (finite variance) and [5] (constant degrees). Results that apply for general
passage time distributions can be found in [11] (power law with infinite mean) and [18](power law with finite mean but infinite variance). Constant passage times are treated in[7, 19].
Other competition models
The two-type frog model was studied in [9] and the competition model driven by branchingrandom walk in [12]. Related competition models on Zd (not mentioned in the presentation) include a two-type version of the contact process introduced in [21], a combinationof first passage percolation and bootstrap percolation [1], two-type branching random
walk with annihilation [2], a model where sites can switch type [20], and competing firstpassage percolation with mutation [22]. A preferential attachment model with two types
is analyzed in [6].

References[1] Ahlberg, D., Griffiths, S., Janson, S. and Morris, R. (2019): Competition in growthand urns, Rand. Struct. Alg. 54, 211-227.
[2] Ahlberg, D., Griffiths, S. and Janson, S. (2021): To fixate or not to fixate in two-type
annihilating branching random walk, Ann. Probab. 49, 2637-2667.
[3] Ahlberg, D., Deijfen, M. and Hoffman, C. (2020): The two-type Richardson modelin the half-plane, Ann. Appl. Probab. 30, 2261-2273.
[4] Ahlberg, D., Deijfen, M. and Janson, S. (2019): Competing first passage percolation
on random graphs with finite variance degrees, Rand. Struct. Alg. 55, 545-559.
[5] Antunovic, T., Dekel, Y., Mossel, E. and Peres, Y. (2017): Competing first passage
percolation on random regular graphs, Rand. Struct. Alg. 50, 534-583.
[6] Antunovic, T., Mossel, E. and Racz, M. (2016): Coexistence in preferential attachment networks, Comb. Probab. Comp. 25, 797-822.
[7] Baroni, E., Komjathy, J. and van der Hofstad, R. (2015): Fixed speed competitionon the configuration model with infinite variance degrees: unequal speeds, Electr. J.
Probab. 20, 1-48.
1[8] Deijfen, M. and Häggström, O. (2007): The pleasures and pains of studying thetwo-type Richardson model, in Analysis and Stochastics of Growth Processes andInterface Models, Oxford University Press, pp 39-54.
[9] Deijfen, M. Hirscher, T. and Lopes, F. (2019): Competing frogs on Zd , Electr. J.
Probab. 24, 1-17.
[10] Deijfen, M. and van der Hofstad, R. (2016): The winner takes it all, Ann. Appl.
Probab. 26, 2419-2453.
[11] Deijfen, M., van der Hofstad, R. and Sfragara, M. (2023+): The winner takes it all
but one, J. Appl. Probab. to appear.
[12] Deijfen, M. and Vilkas, T. (2023): Competition on Z d driven by branching random
walk, Electron. J. Probab. 28, 1-11.
[13] Garet, O. and Marchand, R. (2005): Coexistence in two-type first-passage percolation
models, Ann. Appl. Probab. 15, 298-330.
[14] Garet, O. and Marchand, R. (2007): First-passage competition with different speeds:
positive density for both species is impossible, Electron. J. Probab. 13, 2118-2159.
[15] Häggström, O. and Pemantle, R. (1998): First passage percolation and a model forcompeting spatial growth, J. Appl. Probab. 35, 683-692.
[16] Häggström, O. and Pemantle, R. (2000): Absence of mutual unbounded growth foralmost all parameter values in the two-type Richardson model, Stoch. Proc. Appl.
90, 207-222.
[17] Hoffman, C. (2005): Coexistence for Richardson type competing spatial growth models, Ann. Appl. Probab. 15, 739-747.
[18] van der Hofstad, R. (2023+): Universal ’winner-takes-it-all’ phenomenon in scale-free
random graphs, arxiv.org/abs/2307.09911[19] Komjathy, J. and van der Hofstad, R. (2015): Fixed speed competition on the configuration model with infinite variance degrees: equal speeds, preprint, arxiv:1503.09046.
[20] Kordzakhia, G. and Lalley, S. (2005): A two-species competition model on Zd , Stoch.
Proc. Appl. 115, 781-796.
[21] Neuhauser, C. (1992): Ergodic theorems for the multitype contact process, Probab.
Theory Related Fields 91, 467-506.
[22] Sidoravicius, V. and Stauffer, A. (2016): Multi-particle diffusion limited aggregation,Invent. Math. 218, 491-571.

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