TY - JOUR

T1 - Quantum random walk approximation in Banach algebra

AU - Das, B. Krishna

AU - Lindsay, J. Martin

PY - 2015/10/1

Y1 - 2015/10/1

N2 - Abstract Belton's discrete approximation scheme is extended to Banach-algebra-valued sesquilinear quantum stochastic cocycles, through the dyadic discretisation of time. Approximation results for Markov-regular quantum stochastic mapping cocycles are recovered. We also obtain a new random walk approximation for a class of (not necessarily Markov-regular) isometric operator cocycles. Every Lévy process on a compact quantum group is implemented by a unitary cocycle from this class.

AB - Abstract Belton's discrete approximation scheme is extended to Banach-algebra-valued sesquilinear quantum stochastic cocycles, through the dyadic discretisation of time. Approximation results for Markov-regular quantum stochastic mapping cocycles are recovered. We also obtain a new random walk approximation for a class of (not necessarily Markov-regular) isometric operator cocycles. Every Lévy process on a compact quantum group is implemented by a unitary cocycle from this class.

KW - Noncommutative probability

KW - Quantum random walk

KW - Quantum stochastic cocycle

KW - Quantum Wiener integral

KW - Sesquilinear process

KW - Matrix space

U2 - 10.1016/j.jmaa.2015.02.039

DO - 10.1016/j.jmaa.2015.02.039

M3 - Journal article

VL - 430

SP - 465

EP - 482

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -