A CLASS OF GROWTH MODELS RESCALING TO KPZ

By Martin Hairer, Jeremy Quastel. Forum of Mathematics, Pi, 2015

177 citations recorded by the source corpus.

We consider a large class of $1+1$ -dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf–Cole solutions to the KPZ equation.

Subfields: Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df332db3ff5dad38a1639668fe1fea184e94b665

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Citations in the corpus

The KPZ fixed point (2016, unknown): “ed points. The KPZ equation can be obtained from certain microscopic models in the weakly asymmetric or intermediate disorder limits [BG97;AKQ14;MFQR17;CT17;CN16;CTS16] (which are not equivalent, see [HQ15]). Since some of these models are partially solvable (in particular the asymmetric simple excl”
The Dynamic $${\Phi^4_3}$$Φ34 Model Comes Down from Infinity (2016, methodology): “Related results were obtained for the KPZ equation, first in [2] via a Cole–Hopf transformation, and then, following [22], in a series of works including [11,17,19,20,27,29].”
Algebraic renormalisation of regularity structures (2016, methodology): “hat the maps Πunder consideration are admissible and that the kernels Kt satisfy the assumptions of [Hai14, Sec. 5]. If one considers different notions of admissibility, as is the case for example in [HQ15], then the conclusion of Proposition 6.28 may fail. For a linear Π: T →C∞ we deﬁne Πex : Tex →”