Interacting Particle Systems

By Donald H. House, John Keyser. 2016

1,783 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ef2c37e0ab9bcdbba508b991a15e9b7fd1039e84

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Citations in the corpus

Mean field conditions for coalescing random walks (2011, background): “s for nonreversible chains, for example, random walks on directed graphs. 1.3. Results for the voter model. The voter model is a very well-known process in the interacting particle systems literature [13]. The conﬁguration space for the voter model is the power set OV of functions η :V→O, where 6 R.”
The KPZ fixed point (2016, background): “ nearest neighbour random walks with exclusion: Each particle independently attempts jumps to the neighbouring site to the right at rate 1, the jump being allowed only if that site is unoccupied (see [Lig85] for the non-trivial fact that the process with an inﬁnite number of particles makes sense). ”
Nonlinear Fluctuations of Weakly Asymmetric Interacting Particle Systems (2013, background): “9 of [32] guarantees the existence of the process {ηt; t ≥ 0}.”
From duality to determinants for q-TASEP and ASEP (2012, background): “1 has been known for some time (see [25] Chapter 8, Theorem 1.”
Recent advances in percolation theory and its applications (2015, background): “, contact process [240, 241], epidemic spreading without immunization [242], and forest fire models [243, 244, 245].”
Evolutionary dynamics on any population structure (2016, background): “1 3 A p r i l 2 0 1 7 | V O l 5 4 4 | N A T U r E | 2 2 7 lETTEr doi:10.1038/nature21723 Evolutionary dynamics on any population structure”
Random walks and diffusion on networks (2016, neutral): “consensus probability and mean consensus time [1, 390, 391, 395].”
Competition of tolerant strategies in the spatial public goods game (2016, methodology): “This research was supported by the Hungarian National Research Fund (Grant K-120785) and the Slovenian Research Agency (Grants P5-0027 and J1-7009).”
Models of Social Influence: Towards the Next Frontiers (2017, background): “Sometimes influence of network neighbors is weighted by their individual “social impact” (Latané & L’Herrou 1996; Liggett 1985; Nowak et al. 1990; Parisi et al. 2003).”
Stochastic six-vertex model (2014, background): “ks whether the position to its left is free: if Yes, then it jump by 1 to the left, if No, then nothing happens. Afterwards the clocks are restarted. The ASEP is a very well studied model, cf. [Spi], [Lig1], [Lig2], [TW4], [Cor2]. We are not going to provide the proof, but it is very plausible that ”
Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling (2016, background): “Note that while the hydrodynamic limit for the asymmetric exclusion process on the full line has been well understood for many years [29] (also [3, 26, 30] for the special “wedge” initial condition), the presence of boundary conditions makes the problem more delicate to analyze, and a substantial pa”
Nonequilibrium Markov Processes Conditioned on Large Deviations (2014, background): “modeling systems driven in nonequilibrium steady states by noise and external forces [52–54], such as interacting particle systems coupled to different particle and energy reservoirs, which have been studied actively in the mathematics and physics literature recently [75–79].”
Classical discrete time crystals (2018, background): “[31] In certain special cases [72, 75], it may be possible for a driven, many-body system to avoid its ergodic fate [70].”
On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion (2013, neutral): “This relaxation is not uncommon in probability theory (see for example [Lig85, Sect.”