Noncommutative probability

• 2009 J. Akahori, M. Izumi, S. Watanabe, "Noises, stochastic flows, and E₀-semigroups." AMS Translations, Series 2, Vol. 227 ("selected papers on probability and statistics"), pp. 1-23. [MR2009d:60230]
• 2001 A. Alevras, "The standard form of an E₀-semigroup." J. Funct. Anal. 182:1, 227-242.
• 2004 A. Alevras, "One parameter semigroups of endomorphisms of factors of type II₁." J. Operator Theory 51:1, 161-179.
• 2006 A. Alevras, R.T. Powers, G.L. Price, "Cocycles for one-parameter flows of B(H)." J. Funct. Anal. 230:1, 1-64. [MR2007f:46063]
• 2000 W. Arveson, "Interactions in noncommutative dynamics." Commun. Math. Phys. 211:1, 63-83. [MR2001e:46118] (Also arXiv:math.OA/9910167)
• 2003 W. Arveson, "Four lectures on noncommutative dynamics." Advances in Quantum Dynamics (eds. G.Price et al.), "Contemp. Math." 335, AMS, pp. 1-55. (Also arXiv:math.OA/0207278)
• 2003 W. Arveson, "Noncommutative dynamics and E-semigroups." Springer. [MR2004g:46082 featured review]
• 2004 S. Barreto, B. Bhat, V. Liebscher, M. Skeide, "Type I product systems of Hilbert modules." J. Funct. Anal. 212:1, 121-181.
• 2002 B.V.R. Bhat, "Minimal isometric dilations of operator cocycles." Integral Equations and Operator Theory 42, 125-141.
• 2005 B.V.R. Bhat, "Dilations, cocycles and product systems." Lect. Notes Math. (Springer) 1865, 273-291.
• 2008 B.V.R. Bhat, V. Liebscher, M. Skeide, "A problem of Powers and the product of spatial product systems." arXiv:0801.0042.
• 2010 B.V.R. Bhat, V. Liebscher, M. Skeide, "Subsystems of Fock need not be Fock: spatial CP-semigroups." Proc. AMS 138:7, 2443-2456.
• 2010 B.V.R. Bhat, M. Mukherjee, "Inclusion systems and amalgamated products of product systems." Infin. Dimens. Anal. Quantum Probab. 13:1, 1-26. [MR2011f:46087]
• 2005 B.V.R. Bhat, R. Srinivasan, "On product systems arising from sum systems." Inf. Dim. Anal. Quant. Prob. Rel. Topics 8:1, 1-31. [MR2006e:46075] (Also arXiv:math.OA/0405276.)
• 2008 R. Floricel, "A class of essential representations of product systems." J. Funct. Anal. 255:8, 2067-2089. [MR2462586]
• 2008 R. Floricel, "Infinite tensor products of spatial product systems." Infin. Dimens. Anal. Quantum Probab. 11:3, 447-465. [MR2010b:46145]
• 2008 M. Gregoratti, "Dilations a la Hudson-Parthasarathy of Markov semigroups in classical probability." Stoch. Anal. Appl. 26:5, 1025-1052. [MR2440914]
• 2004 J. Hellmich, C. Koestler, B. Kuemmerer, "Non-commutative continuous Bernoulli shifts." arXiv:math.OA/0411565.
• 2007 M. Izumi, "A perturbation problem for the shift semigroup." J. Funct. Anal. 251:2, 498-545. [MR2356422] (Also arXiv:math.OA/0702439.)
• 2009 M. Izumi, "Every sum system is divisible." Trans. Amer. Math. Soc. 361:8, 4247-4267. [MR2500888] (Also arXiv:0708.1591.)
• 2008 M. Izumi, R. Srinivasan, "Generalized CCR flows." Commun. Math. Phys. 281:2, 529-571. [MR2009c:46096] (Also arXiv:0705.3280.)
• 2010 M. Izumi, R. Srinivasan, "Toeplitz CAR flows and type I factorizations." Kyoto J. Math. 50:1, 1-32. (Also arXiv:0906.1872.)
• 2009 C. Jankowski, "On type II₀ E₀-semigroups induced by boundary weight doubles." arXiv:0905.2708.
• 2010 C. Jankowski, "Unital q-positive maps on M₂(C) and a related E₀-semigroup result." arXiv:1005.4404.
• 2010 C. Jankowski, "A family of non-cocycle conjugate E₀-semigroups obtained from boundary weight doubles." arXiv:1007.4459.
• 2004 P.E.T. Jorgensen, "Iterated function systems, representations, and Hilbert space." Internat. J. Math. 15:8, 813-832. [MR2005h:28021]
• 2007 G. Kalai, "Is the Universe noise sensitive?" arXiv:hep-th/0703092.
• 2007 C. Koestler, R. Speicher, "On the structure of non-commutative white noises." Trans. Amer. Math. Soc. 359:9, 4325-4338. [MR2309187]. (Also arXiv:math.OA/0411519.)
• 2009 V. Liebscher, "Random sets and invariants for (type II) continuous tensor product systems of Hilbert spaces." Memoirs Amer. Math. Soc., no. 930. [MR2507929]. (Also arXiv:math.PR/0306365.)
• 2003 D. Markiewicz, "On the product system of a completely positive semigroup." J. Funct. Anal. 200:1, 237-280.
• 2009 D. Markiewicz, R.T. Powers, "Local unitary cocycles of E₀-semigroups." J. Funct. Anal. 256:5, 1511-1543. [MR2490228]. (Also arXiv:0805.2821.)
• 2004 P.S. Muhly, M. Skeide, B. Solel, "Representations of B^a(E)." Infin. Dimens. Anal. Quantum Probab. 9:1, 47-66. (Also arXiv:math.OA/0410607.)
• 2003 R.T. Powers, "Continuous spatial semigroups of completely positive maps of B(H)." New York J. Math. 9, 165-269. [MR2005c:46099]
• 2006 M. Skeide, "The index of (white) noises and their product systems." Infin. Dimens. Anal. Quantum Probab. 9:4, 617-655. Also arXiv:math.OA/0601228.
• 2006 M. Skeide, "A simple proof of the fundamental theorem about Arveson systems." Infin. Dimens. Anal. Quantum Probab. 9:2, 305-314. (Also arXiv:math.OA/0602014v2.)
• 2007 M. Skeide, "Product systems: a survey with commutants in view." arXiv:0709.0915.
• 2008 M. Skeide, "Spatial Markov semigroups admit Hudson-Parthasarathy dilations." arXiv:0809.3538.
• 2008 A.M. Vershik, M.I. Graev, "Integral models of unitary representations of current groups with values in semidirect products." Funct. Anal. Appl. 42:4, 279-289. [MR2492425]
• 2009 A.M. Vershik, M.I. Graev, "Integral models of representations of the current groups of simple Lie groups." Russian Math. Surveys 64:2, 205-271.
• 2003 A. Vershik, N. Tsilevich, "Fock factorizations, and decompositions of the L² spaces over general Levy processes." Russian Math. Surveys 58:3, 427-472. (Also arXiv:math.PR/0304282.)
• 2005 A. Vourdas, "Propagation of a quantum state in a continuum of coupled oscillators and applications to entanglement." J. Phys. A 38, 9859-9875.
• 2010 V.I. Yukalov, "Turbulent superfluid as continuous vortex mixture." Laser Phys. Lett. 7:6, 467-476.
• 2000 J. Zacharias, "Pure infiniteness of spectral algebras." J. Funct. Anal. 178:2, 381-395.