caa a22 4500 44539157X CHVBK 20180317143048.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10955-010-0098-2 doi (NATIONALLICENCE)springer-10.1007/s10955-010-0098-2 Two-dimensional Quantum Random Walk [Elektronische Daten] [Yuliy Baryshnikov, Wil Brady, Andrew Bressler, Robin Pemantle] We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting shape of the feasible region is, however, quite different. The limit region turns out to be an algebraic set, which we characterize as the rational image of a compact algebraic variety. We also compute the probability profile within the limit region, which is essentially a negative power of the Gaussian curvature of the same algebraic variety. Our methods are based on analysis of the space-time generating function, following the methods of Pemantle and Wilson (J. Comb. Theory, Ser. A 97(1):129-161, 2002). Springer Science+Business Media, LLC, 2010 Rational generating function nationallicence Amoeba nationallicence Saddle point nationallicence Stationary phase nationallicence Residue nationallicence Fourier-Laplace nationallicence Gauss map nationallicence Baryshnikov Yuliy Lucent Technologies, Bell Laboratories, 700 Mountain Avenue, 07974-0636, Murray Hill, NJ, USA aut Brady Wil 1 Microsoft Way, 98052, Redmond, WA, USA aut Bressler Andrew Dept. of Mathematics, University of Pennsylvania, 209 South 33rd Street, 19104, Philadelphia, PA, USA aut Pemantle Robin Department of Mathematics, University of Pennsylvania, 209 S. 33rd Street, 19104, Philadelphia, PA, USA aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/1(2011-01-01), 78-107 0022-4715 142:1<78 2011 142 10955 https://doi.org/10.1007/s10955-010-0098-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-010-0098-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baryshnikov Yuliy Lucent Technologies, Bell Laboratories, 700 Mountain Avenue, 07974-0636, Murray Hill, NJ, USA aut NATIONALLICENCE 700 1- Brady Wil 1 Microsoft Way, 98052, Redmond, WA, USA aut NATIONALLICENCE 700 1- Bressler Andrew Dept. of Mathematics, University of Pennsylvania, 209 South 33rd Street, 19104, Philadelphia, PA, USA aut NATIONALLICENCE 700 1- Pemantle Robin Department of Mathematics, University of Pennsylvania, 209 S. 33rd Street, 19104, Philadelphia, PA, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/1(2011-01-01), 78-107 0022-4715 142:1<78 2011 142 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer