Michael Anshelevich

Office: Blocker 533D

Email address: manshel math.tamu.edu
Department of Mathematics
Texas A&M University
College Station TX 77843-3368

Foundations of Mathematics: Math 220

Undergraduate research

Linear Analysis seminar

Free probability seminar

Professional links


Rarely updated pages


With one (free electronic) exception, older versions of these papers are available at the
Mathematics arXiv.
  1. Higher variations for free Lévy processes (with Zhichao Wang), arXiv:1811.00456 [math.OA].
  2. Product formulas on posets, Wick products, and a correction for the q-Poisson process, arXiv:1708.08034 [math.OA].
  3. Operator-valued Jacobi parameters and examples of operator-valued distributions (with John D. Williams), Bull. Sci. Math. 145 (2018) 1-37.
  4. Expansion of permutations as products of transpositions (with Matthew Gaikema, Madeline Hansalik, Songyu He, and Nathan Mehlhop), arXiv:1702.06093 [math.CO].
  5. The exponential map in non-commutative probability (with Octavio Arizmendi), Int. Math. Res. Notices 2017 (17), 5302-5342.
  6. Operator-Valued Monotone Convolution Semigroups and an Extension of the Bercovici-Pata Bijection (with John D. Williams), Doc. Math. 21 (2016) 841-871.
  7. A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind, Integral Transforms And Special Functions 27 (2016) 307-317.
  8. Free evolution on algebras with two states II, Pacific J. Math. 276 (2015) 257-280.
  9. Local limit theorems for multiplicative free convolutions (with JC Wang and Ping Zhong), J. Funct. Anal. 267 (2014), 3469-3499.
  10. Limit theorems for monotonic convolution and the Chernoff product formula (with John D. Williams), Int. Math. Res. Notices 2014 (11), 2990-3021. A version with more general results is at arXiv:1209.4260 [math.OA].
  11. Convolution powers in the operator-valued framework (with Serban T. Belinschi, Maxime Fevrier, and Alexandru Nica), Trans. Amer. Math. Soc. 365 (2013), 2063-2097.
  12. Generators of some non-commutative stochastic processes, Probab. Theory Related Fields 157 (2013), 777-815.
  13. Quantum free Yang-Mills on the plane (with Ambar N. Sengupta), J. Geom. Phys. 62 (2012) 330-343.
  14. Semigroups of distributions with linear Jacobi parameters (with Wojciech Młotkowski), J. Theoret. Probab. 25 (2012), 1173-1206.
  15. Two-state free Brownian motions, J. Funct. Anal. 260 (2011), 541-565.
  16. Bochner-Pearson-type characterization of the free Meixner class, Adv. in Appl. Math. 46 (2011), 25-45 (special issue in honor of Dennis Stanton).
  17. Free infinite divisibility for q-Gaussians (with Serban Teodor Belinschi, Marek Bożejko, and Franz Lehner), Math. Res. Lett. 17 (2010), 905-916.
  18. Product-type non-commutative polynomial states, Noncommutative Harmonic Analysis with Applications to Probability II, Banach Center Publ., vol. 89, Polish Acad. Sci. Inst. Math., Warsaw, 2010, pp. 45-59.
  19. Free evolution on algebras with two states, J. Reine Angew. Math. 638 (2010), 75-101.
  20. Appell polynomials and their relatives III. Conditionally free theory, Illinois J. Math. 53 (2009), 39-66.
  21. Appell polynomials and their relatives II. Boolean theory, Indiana Univ. Math. J. 58 (2009), 929-968.
  22. Monic non-commutative orthogonal polynomials, Proc. Amer. Math. Soc. 136 (2008), 2395-2405.
  23. Orthogonal polynomials with a resolvent-type generating function, Trans. Amer. Math. Soc. 360 (2008), 4125-4143.
  24. Free Meixner states, Commun. Math. Phys. 276 (2007), 863-899.
  25. Zimmermann type cancellation in the free Faà di Bruno algebra (with Edward G. Effros and Mihai Popa), J. Funct. Anal. 237 (2006), 76-104.
  26. Linearization coefficients for orthogonal polynomials using stochastic processes, Ann. Probab. 33 (2005), 114-136.
  27. q-Lévy processes, J. Reine Angew. Math. 576 (2004), 181-207.
  28. Appell polynomials and their relatives, Int. Math. Res. Not. 2004 n. 65, 3469-3531. Maple worksheet used in the Appendix. A more complete version of the paper is at arXiv:math/0311043 [math.CO].
  29. Free martingale polynomials, J. Funct. Anal. 201 (2003), 228-261.
  30. Itô formula for free stochastic integrals, J. Funct. Anal. 188 (2002), 292-315.
  31. Free stochastic measures via noncrossing partitions II, Pacific J. Math. 207 (2002), 13-30.
  32. Partition-dependent stochastic measures and q-deformed cumulants, Doc. Math. 6 (2001), 343-384.
  33. Free stochastic measures via noncrossing partitions, Adv. Math. 155 (2000), 154-179.
  34. The linearization of the central limit operator in free probability theory, Probab. Theory Related Fields 115 (1999), 401-416.


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