Publications

In 2023 I published a book, “The mathematics of shuffling cards“, written jointly with Persi Diaconis. I was interviewed about this book: “Jason Fulman, The best and worst ways to shuffle a deck of cards”

Here are some other publications. This list is not necessarily up to date or complete. Only the published versions are definitive.

• Stein’s method and the modular behavior of Eulerian numbers, joint with Adrian Roellin, preprint available on the archives.
• Derangements in affine classical groups and Cohen-Lenstra heuristics, joint with Dennis Stanton, Journal of Algebra, Volume 697 (2026), 52-62.
• Derangements in finite classical groups and characteristic polynomials of random matrices, joint with Robert Guralnick, Journal of Algebra, Volume 698, (2026), 116-137.
• Representation theory and central limit theorems for traces of commutators for compact Lie groups, Advances in Applied Math, Volume 172, 2026, 10 pages.
• Tensor product Markov chains and Weil representations, joint with Michael Larsen and Pham Huu Tiep, Journal of Algebra, 2025, 278-314.
• Fixed points of non-uniform permutations and representation theory of the symmetric group (On the archives but not intended for publication)
• Probabilistic generation of finite almost simple groups, joint with Daniele Garzoni and Robert Guralnick, Advances in Mathematics, 2024, 26 pages.
• Beta approximation for the two alleles Moran model by Stein’s method, Statistics and Probability Letters, 2024, 7 pages
• Carries and a map on the space of rational functions, Advances in Applied Mathematics, Volume 152, 2024, 7 pages.
• Enumeration of conjugacy classes in affine groups, joint with Robert Guralnick, Algebra and Number Theory, Volume 18, 2024, 1189-1219.
• Cohen-Lenstra partitions and mutually annihilating matrices over a finite field, joint with Robert Guralnick, Linear Algebra and its Applications, Volume 645, 2022, 1-8.
• Card shuffling and P-partitions, joint with T. Kyle Petersen, Discrete Mathematics, Volume 344, 2021, 18 pages
• On the joint distribution of descents and signs of permutations, joint with Gene B. Kim, Sangchul Lee, and T. Kyle Petersen, Electronic Journal of Combinatorics, Volume 28, 2021, 30 pages
• Central limit theorem for peaks of a random permutation in a fixed conjugacy class of Sn, joint with Gene B. Kim and Sangchul Lee, Annals of Combinatorics, Volume 26, 2022, 97-123.
• Stein’s method, heat kernel, and linear functions on the orthogonal groups , joint with Adrian Roellin, Journal of Algebra, Volume 607, 2022, 272-285
• Stein’s method and Narayana numbers, joint with Adrian Roellin, Statistics and Probability Letters, Volume 165, 2020, 9 pages
• Random partitions and Cohen-Lenstra heuristics, joint with Nathan Kaplan, Annals of Combinatorics, Volume 23 (2019), 295-315.
• Enumeration of Commuting Pairs in Lie Algebras over Finite Fields, joint with Robert Guralnick, Annals of Combinatorics, Volume 22 (2018), 295-316.
• Generating functions and statistics on spaces of maximal tori in classical Lie groups, joint with Rita Jimenez Rolland and Jennifer Wilson, New York Journal of Mathematics, Volume 23, 2017, pages 165-191.
• Derangements in finite classical groups for actions related to extension field and imprimitive subgroups and the solution of the Boston-Shalev conjecture, joint with Robert Guralnick, Transactions of the American Math Society, Volume 370, 2018, 4601-4622.
• Asymptotics of the number of involutions in finite classical groups , joint with Robert Guralnick and Dennis Stanton, Journal of Group Theory, Volume 20, 2017, pages 871-902.
• On the distribution of the number of fixed vectors for the finite classical groups, joint with Dennis Stanton, Annals of Combinatorics, Volume 20 (2016), 755-773.
• A generating function approach to counting theorems for square-free polynomials and maximal tori, Annals of Combinatorics, Volume 20, (2016), pages 587-599.
• Stein’s method, semicircle distribution, and reduced decompositions of the longest element in the symmetric group, joint with Larry Goldstein, not intended for publication.
• Hall-Littlewood polynomials and Cohen-Lenstra heuristics for Jacobians of random graphs, Annals of Combinatorics, Volume 20, 2016, pages 115-124.
• Combinatorics of balanced carries , joint with Persi Diaconis, Advances in Applied Math, Volume 59 (2014), 8-25
• Cohen-Lenstra heuristics and random matrix theory over finite fields, Journal of Group Theory, Volume 17 (2014), 619-648.
• Generating functions for real character degree sums of finite general linear and unitary groups, joint with Ryan Vinroot, Journal of Algebraic Combinatorics, Volume 40 (2014), 387-416.
• Derangements in subspace actions of finite classical groups, joint with Robert Guralnick, Transactions of American Math Society, Volume 369 (2017), no. 4, 2521-2572.
• Stein’s method and the rank distribution of random matrices over finite fields, joint with Larry Goldstein, Annals of Probability, Vol. 43 (2015), 1274-1314.
• The number of regular semisimple conjugacy classes in the finite classical groups, joint with Robert Guralnick, Linear Algebra and its Applications, Volume 439 (2013), 488-503. joint with Nathan Ross, ALEA, Lat. Am. J. Probab. Math. Stat., Volume 10 (2013), 1-13.
• Exponential approximation and Stein’s method of exchangeable pairs, joint with Nathan Ross, ALEA, Lat. Am. J. Probab. Math. Stat., Volume 10 (2013), 1-13..
• Analysis of Casino Shelf Shuffling Machines, joint with Persi Diaconis and Susan Holmes, Annals of Applied Probability, Vol. 23, No. 4, (2013), 1692-1720.
• Foulkes Characters, Eulerian Idempotents, and an Amazing Matrix, joint with Persi Diaconis, Journal of Algebraic Combinatorics, Volume 36, Issue 3 (2012), 425-440.
• Zero biasing and Jack measures, (pdf file) joint with Larry Goldstein, Combinatorics, Probability, and Computing, Volume 20, 2011, 753-762.
• Stein’s method, heat kernel, and traces of powers of elements of compact Lie groups, Electronic Journal of Probability, 17 (2012), no. 66, 1-16.
• Cycle indices for finite orthogonal groups of even characteristic (pdf file) joint with Jan Saxl and Pham Huu Tiep, Transactions of American Math Society, Volume 364, 2012, 2539-2566.
• On adding a list of numbers (and other one-dependent determinantal processes) (pdf file) joint with Alexei Borodin and Persi Diaconis, Bulletin of the American Mathematical Society, Volume 47, 2010, 639-670.
• Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements (pdf file) joint with Robert Guralnick, Transactions of the American Math Society, Volume 364, 2012, 3023-3070.
• Mixing time for random walk on rooted trees, Electronic Journal of Combinatorics, Volume 16 (1), R 139, 2009, 13 pages.
• Carries, shuffling, and symmetric functions (pdf file) joint with Persi Diaconis, Advances in Applied Math, Volume 43 (2009), 176-196.
• Carries, shuffling, and an amazing matrix (pdf file) joint with Persi Diaconis, American Math Monthly, Volume 116 (2009), 788-803.
• Stein’s method and characters of compact Lie groups (pdf file), Communications of Mathematical Physics Vol. 288, 1181-1201.
• Commutation relations and Markov chains (pdf file), Probab. Theory Rel. Fields Vol. 144, 99-136 (2009).
• On fixed points of permutations, (pdf file) joint with Persi Diaconis and Robert Guralnick, Journal of Algebraic Combinatorics, Volume 28 (2008), 189-218.
• Separation cutoffs for random walk on irreducible representations. (pdf file), Annals of Combinatorics Vol. 14, 319-337 (2010).
• Convergence rates of random walk on irreducible representations of finite groups. (pdf file), Journal of Theoretical Probability, Volume 21 (2008), 193-211
• Exponential approximation by Stein’s method and spectral graph theory. (pdf file), joint with Sourav Chatterjee and Adrian Rollin, ALEA, Lat. Am. J. Probab. Math. Stat., Volume 8 (2011), 197-223
• Stein’s method and random character ratios. (pdf file), Transac. Amer. Math. Soc., Volume 360 (2008), 3687-3730.
• An inductive proof of the Berry-Esseen theorem for character ratios. (pdf file), Annals of Combinatorics, Volume 10 (2006), 319-332
• Power series coefficients for probabilities in finite classical groups. (pdf file), joint with John Britnell, , Journal of Algebra, Volume 305 (2006), 1212-1237.
• Martingales and character ratios. (pdf file), Transac. Amer. Math. Soc., Volume 358 (2006), 4533-4552.
• Stein’s method and descents after riffle shuffles. (pdf file), Electronic Journal of Probability, Volume 10 (2005), paper no. 26, pages 901-924.
• A generating function approach to matrix enumeration in classical groups over finite fields; (pdf file), joint with Peter M. Neumann and Cheryl E. Praeger, Memoirs Amer. Math. Soc., Volume 176, No. 830 (2005).
• Stein’s method and Plancherel measure of the symmetric group (pdf file); Transac. Amer. Math. Soc., Volume 357 (2005), 555-570.
• Card shuffling and the decomposition of tensor products. (pdf file); Pacific J. Math., Volume 217 (2004), pages 247-262.
• Stein’s method, Jack measure, and the Metropolis algorithm. (pdf file) ; Journal of Combinatorial Theory, Series A, Volume 108 (2004), pages 275-296.
• Conjugacy class properties of the extension of GL(n,q) generated by the inverse transpose involution ; (pdf file), joint with Robert Guralnick, Journal of Algebra, Volume 275 (2004), 356-396.
• A Card shuffling analysis of deformations of the Plancherel measure of the symmetric group (pdf file) , Electron. Journal of Combinatorics, Volume 11, 2004.
• Derangements in simple and primitive groups ; joint with Robert Guralnick, in Groups, combinatorics, and geometry: Durham 2001, pages 99-121, Ivanov, Liebeck and Saxl editors .
• Stein’s Method and Non-Reversible Markov Chains; pages 69-77 in Institute of Mathematical Statistics Lecture Notes. Volume 46, “Stein’s Method: Expository Lectures and Applications” (2004)
• Applications of Symmetric Functions to Cycle and Increasing Subsequence Structure After Shuffles , Journal of Algebraic Combinatorics, Volume 16 (2002), 165-194.
• GL(n,q) and Increasing Subsequences in Nonuniform Random Permutations; Annals of Combinatorics. Volume 6 (2002), 19-32.
• Finite Affine Groups: Cycle Indices, Symmetric Functions, and Probabilistic Algorithms; Journal of Algebra. Volume 250, 2002, 731-756.
• Random Matrix Theory over Finite Fields. Bulletin of the American Mathematical Society. Volume 39, 2002, 51-85.
• Applications of the Brauer Complex: Card Shuffling, Permutation Statistics, and Dynamical Systems; (dvi file) Journal of Algebra Volume 243, 2001, 96-122.
• A Probabilistic Proof of the Rogers Ramanujan Identities; Bulletin of the London Math Society, Volume 33, 2001, 397-407
• Descent Algebras, Hyperplane Arrangements and Shuffing Cards. Proceedings of the American Mathematical Society Volume 129, 2001, 965-973
• A Probabilistic Approach to Conjugacy Classes in the Finite Symplectic and Orthogonal Groups; Journal of Algebra. Volume 234, 2000, 207-224.
• Affine Shuffles, Shuffles with Cuts, the Whitehouse module, and Patience Sorting; Journal of Algebra, Volume 231, 2000, 614-639.
• The Eigenvalue Distribution of a Random Finite Unipotent Matrix in its Action on Lines; Journal of Algebra. Volume 228, 2000, 497-511
• Counting Nilpotent pairs in Finite Groups (joint with Mike Galloy, Gary Sherman, and Jeff Vanderkam); Ars Combinatoria. Volume 54, 2000, 161-178
• Semisimple Orbits of Lie Algebras and Card Shuffling Measures on Coxeter Groups; Journal of Algebra. Bolume 224, 2000, 151-165.
• Descent Identites, Hessenberg Varieties and the Weil Conjectures; Journal of Combinatoial Theory, Series A. Volume 87, 1999, 390-397
• Comparing EigenValue Bounds for Markov Chains: When Does Poincare beat Cheeger? (joint with Elizabeth Wilmer); Annals of Applied Probability. Volume 9, 1999, 1-13
• Counting Semisimple Orbits of Finite Lie Algebras by Genus; Journal of Algebra.Volume 217, 1999, 170-179
• Cycle Indices for the Finite Classical Groups; Journal of Group Theory. Volume 2, Issue 3, 1999, pages 251-289.
• A Probabilistic Approach Toward Conjugancy Classes in the Finite General Linear and Unitary Groups, Journal of Algebra, Volume 212, No.2, 1999, 557-590
• A Simple Geometric Proof of the Invariance of the Conway Polynomial for Links in 3-Space (joint with Dror Bar-Natan and Lou Kauffman). Journal of Knot theory and its Ramifications. Volume 7, No. 7 (1998), pages 873-879.
• The Combinatorics of Biased Riffle Shuffles. Combinatorica. Volume 18, No.2, 1998. pages 173-184.
• Orbifold Euler Characteristics and the Number of Computing m-tuples in the Symmetric Groups (joint with Jim Bryan). Annals of Combinatorics. Volume 2, 1998, pages 1-6.65/
• Probability in the Classical Groups over Finite Fields: Symmetric Functions, Probabilistic Algorithms, and Cycle Indices . phD Thesis, Harvard University, 1997.