Journal of Statistical Physics

, Volume 160, Issue 4, pp 794–814 | Cite as

A KPZ Cocktail-Shaken, not Stirred...

Toasting 30 Years of Kinetically Roughened Surfaces
  • Timothy Halpin-HealyEmail author
  • Kazumasa A. Takeuchi


The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we (i) pay debts to heroic predecessors, (ii) highlight additional, experimentally relevant aspects of the recently solved 1+1 KPZ problem, (iii) use an expanding substrates formalism to gain access to the 3d radial KPZ equation and, lastly, (iv) examining extremal paths on disordered hierarchical lattices, set our gaze upon the fate of \(d=\infty \) KPZ. Clearly, there remains ample unexplored territory within the realm of KPZ and, for the hearty, much work to be done, especially in higher dimensions, where numerical and renormalization group methods are providing a deeper understanding of this iconic equation.


Nonequilibrium growth Extremal paths Universal limit distributions 



The authors would like to express their gratitude to Herbert Spohn for his many years of inspired work, wisdom, and stamina on behalf of the KPZ cause. Thanks, too, to Joel Lebowitz for keeping the statistical mechanical fire well-lit through the generations. This work is supported in part by KAKENHI (No. 25707033 from JSPS and No. 25103004 “Fluctuation & Structure” from MEXT in Japan).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Physics, Barnard CollegeColumbia UniversityNew YorkUSA
  2. 2.Department of PhysicsUniversity of TokyoBunkyo-kuJapan
  3. 3.Department of PhysicsTokyo Institute of TechnologyMeguro-kuJapan

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