The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality
Open accessAbstract
We report on the first exact solution of the Kardar-Parisi-Zhang (KPZ) equation in one dimension, with an initial condition which physically corresponds to the motion of a macroscopically curved height profile. The solution provides a determinantal formula for the probability distribution function of the height h(x,t) for all t>0. In particular, we show that for large t, on the scale t(1/3), the statistics is given by the Tracy-Widom distribution, known already from the Gaussian unitary ensemble of random matrix theory. Our solution confirms that the KPZ equation describes the interface motion in the regime of weak driving force. Within this regime the KPZ equation details how the long time asymptotics is approached.
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Citations
Cites
Dynamic Scaling of Growing Interfaces
Kardar, M., Parisi, G., & Zhang, Y.-C. (1986) · Physical Review Letters · doi:10.1103/physrevlett.56.889 · Cited by 5,380
Fractal Concepts in Surface Growth
Barabási, A. L., & Stanley, H. E. (1995) · doi:10.1017/cbo9780511599798 · Cited by 3,925
Fractal Concepts in Surface Growth
Barabasi, A. L., Stanley, H. E., & Sander, L. M. (1995) · Physics Today · doi:10.1063/1.2808215 · Cited by 3,290
Level-spacing distributions and the Airy kernel
Tracy, C. A., & Widom, H. (1994) · Communications in Mathematical Physics · doi:10.1007/bf02100489 · Cited by 1,828
Halpin-Healy, T., & Zhang, Y.-C. (1995) · Physics Reports · doi:10.1016/0370-1573(94)00087-j · Cited by 1,443
On the distribution of the length of the longest increasing subsequence of random permutations
Baik, J., Deift, P., & Johansson, K. (1999) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-99-00307-0 · Cited by 1,148
Origins of scale invariance in growth processes
Krug, J. (1997) · Advances in Physics · doi:10.1080/00018739700101498 · Cited by 1,016
The spectrum edge of random matrix ensembles
Forrester, P. J. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90126-a · Cited by 517
Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
Takeuchi, K. A., & Sano, M. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.230601 · Cited by 368
On the numerical evaluation of Fredholm determinants
Bornemann, F. (2009) · Mathematics of Computation · doi:10.1090/s0025-5718-09-02280-7 · Cited by 281
Metadata
- Authors
- Sasamoto, T., & Spohn, H.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-06-11
- Volume
- 104
- Issue
- 23
- Pages
- 230602-230602
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1577096229
- Cited by
- 451
- References
- 11
- FWCI
- 38.38
- Type
- journal article
- Language
- en
- Open access
- green
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- Sasamoto, T., & Spohn, H. (2010). One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality. Physical Review Letters. https://doi.org/10.1103/physrevlett.104.230602
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