Abstract
Packed initial conditions turn out to be the most readily accessible case. Although such initial conditions have been studied extensively in the literature, we provide here a complete proof, introducing essentially all methods required later on in more complicated situations. The second treatable case of deterministic initial data are periodic initial conditions. Here we will be rather brief, in stating only the main results, since the tools used in Ferrari et al. (2015) (Ferrari et al., Ann. Appl. Probab. 25, 1349–1382, 2015) are comparable to the ones employed in case of packed initial conditions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
P.L. Ferrari, H. Spohn, T. Weiss, Scaling limit for Brownian motions with one-sided collisions. Ann. Appl. Probab. 25, 1349–1382 (2015)
J. Warren, Dyson’s Brownian motions, intertwining and interlacing. Electron. J. Probab. 12, 573–590 (2007)
A. Borodin, P.L. Ferrari, M. Prähofer, T. Sasamoto, Fluctuation properties of the TASEP with periodic initial configuration. J. Stat. Phys. 129, 1055–1080 (2007)
J. Gravner, C.A. Tracy, H. Widom, Limit theorems for height fluctuations in a class of discrete space and time growth models. J. Stat. Phys. 102, 1085–1132 (2001)
Y. Chen, K.L. Moore, Analytical stability bound for delayed second-order systems with repeating poles using Lambert function W. Automatica 38, 891–895 (2002)
T.C. Banwell, A. Jayakumar, Exact analytical solution for current flow through diode with series resistance. Electron. Lett. 36, 291–292 (2000)
A. Jain, A. Kapoor, Exact analytical solutions of the parameters of real solar cells using Lambert W-function. Solar Energy Mater. Solar Cells 81, 269–277 (2004)
R.M. Corless, D.J. Jeffrey, S.R. Valluri, Some applications of the Lambert W function to physics. Canadian J. Phys. 78, 823–831 (2000)
D.A. Barry, J.-Y. Parlange, L. Li, H. Prommer, C.J. Cunningham, F. Stagnitti, Analytical approximations for real values of the Lambert W-function. Math. Comput. Simul. 53, 95–103 (2000)
R.M. Corless, D.J. Jeffrey, D.E. Knuth, A sequence of series for the Lambert W function, in Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (1997), pp. 197–204
R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, Lambert’s W function in maple. Maple Tech. Newsl. 9, 12–22 (1993)
R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth, On the Lambert W function. Adv. Comput. Math. 5, 329–359 (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
Weiss, T., Ferrari, P., Spohn, H. (2017). Packed and Periodic Initial Conditions. In: Reflected Brownian Motions in the KPZ Universality Class. SpringerBriefs in Mathematical Physics, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-49499-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-49499-9_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49498-2
Online ISBN: 978-3-319-49499-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)