Papers

See also my Google Scholar profile.

Selected papers

All papers

Journal papers

  1. D. Romik. On Viazovska's modular form inequalities. Proceedings of the National Academy of Sciences USA, vol. 120, article e2304891120, 2023.
  2. E. Bisi, F. D. Cunden, S. Gibbons, and D. Romik. The oriented swap process and last passage percolation. Random Structures & Algorithms, vol. 60, pp. 690-715, 2022.
  3. A. Bufetov, V. Gorin, and D. Romik. Absorbing time asymptotics in the oriented swap process. Annals of Applied Probability, vol. 32, pp. 753-763, 2022.
  4. D. Romik. Orthogonal polynomial expansions for the Riemann xi function in the Hermite, Meixner-Pollaczek, and continuous Hahn bases. Acta Arithmetica, vol. 200, pp. 259-329, 2021.
  5. D. Romik and R. Scherer. Alternative summation orders for the Eisenstein series G₂ and Weierstrass ℘-function. Rocky Mountain Journal of Mathematics, vol. 50, pp. 1473-1482, 2020.
  6. D. Romik. The Taylor coefficients of the Jacobi theta constant θ₃. Ramanujan Journal, vol. 52, pp. 275-290, 2020.
  7. Y. Kallus and D. Romik. Improved upper bounds in the moving sofa problem. Advances in Mathematics, vol. 340, pp. 960-982, 2018.
  8. D. Romik. Differential equations and exact solutions in the moving sofa problem. Experimental Mathematics, vol. 27, pp. 316-330, 2018.
  9. D. Romik. On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function. Acta Arithmetica, vol. 180, pp. 111-159, 2017.
  10. R. Peled and D. Romik. Bijective combinatorial proof of the commutation of transfer matrices in the dense O(1) loop model. Séminaire Lotharingien de Combinatoire, vol. 73, article B73b, 2015.
  11. D. Romik and P. Śniady. Limit shapes of bumping routes in the Robinson-Schensted correspondence. Random Structures & Algorithms, vol. 48, pp. 171-182, 2016.
  12. D. Romik. Connectivity patterns in loop percolation I: the rationality phenomenon and constant term identities. Communications in Mathematical Physics, vol. 330, pp. 499-538, 2014.
  13. D. Romik and P. Śniady. Jeu de taquin dynamics on infinite Young tableaux and second class particles. Annals of Probability, vol. 43, pp. 682-737, 2015.
  14. A. Ayyer and D. Romik. New enumeration formulas for alternating sign matrices and square ice partition functions. Advances in Mathematics, vol. 235, pp. 161-186, 2013.
  15. D. Romik. Arctic circles, domino tilings and square Young tableaux. Annals of Probability, vol. 40, pp. 611-647, 2012.
  16. S. Chatterjee, R. Peled, Y. Peres, and D. Romik. Phase transitions in gravitational allocation. Geometric and Functional Analysis, vol. 20, pp. 870-917, 2010.
  17. M. Karklinsky and D. Romik. A formula for a doubly refined enumeration of alternating sign matrices. Advances in Applied Mathematics, vol. 45, pp. 28-35, 2010.
  18. I. Fischer and D. Romik. More refined enumerations of alternating sign matrices. Advances in Mathematics, vol. 222, pp. 2004-2035, 2009.
  19. O. Angel, A. Holroyd, and D. Romik. The oriented swap process. Annals of Probability, vol. 37, pp. 1970-1998, 2009.
  20. Y. Baryshnikov and D. Romik. Enumeration formulas for Young tableaux in a diagonal strip. The Israel Journal of Mathematics, vol. 178, pp. 157-186, 2010.
  21. S. Chatterjee, R. Peled, Y. Peres, and D. Romik. Gravitational allocation to Poisson points. Annals of Mathematics, vol. 172, pp. 617-671, 2010.
  22. O. Angel, A. Holroyd, B. Virág, and D. Romik. Random sorting networks. Advances in Mathematics, vol. 215, pp. 839-868, 2007.
  23. D. Romik. The dynamics of Pythagorean triples. Transactions of the American Mathematical Society, vol. 360, pp. 6045-6064, 2008.
  24. G. Andrews, H. Eriksson, F. Petrov, and D. Romik. Integrals, probability, and MacMahon's theorem. Journal of Combinatorial Theory Series A, vol. 114, pp. 545-554, 2007.
  25. N. Harvey, A. Holroyd, Y. Peres, and D. Romik. Universal finitary codes with exponential tails. Proceedings of the London Mathematical Society, vol. 94, pp. 475-496, 2007.
  26. D. Romik. Shortest paths in the Tower of Hanoi graph and finite automata. SIAM Journal on Discrete Mathematics, vol. 20, pp. 610-622, 2006.
  27. E. Ackerman, G. Barequet, R. Pinter, and D. Romik. The number of guillotine partitions in d dimensions. Information Processing Letters, vol. 98, pp. 162-167, 2006.
  28. I. Benjamini, G. Kozma, and D. Romik. Random walks with k-wise independent increments. Electronic Communications in Probability, vol. 11, pp. 100-107, 2006.
  29. B. Pittel and D. Romik. Limit shapes for random square Young tableaux. Advances in Applied Mathematics, vol. 38, pp. 164-209, 2007.
  30. D. Romik. Permutations with short monotone subsequences. Advances in Applied Mathematics, vol. 37, pp. 501-510, 2006.
  31. I. Benjamini, G. Kozma, L. Lovász, G. Tardos, and D. Romik. Waiting for a bat to fly by (in polynomial time). Combinatorics, Probability and Computing, vol. 15, pp. 673-683, 2006.
  32. D. Romik. Roots of the derivative of a polynomial. American Mathematical Monthly, vol. 112, pp. 66-68, 2005.
  33. D. Romik. Some formulas for the central trinomial and Motzkin numbers. Journal of Integer Sequences, vol. 6, article 03.2.3, 2003.
  34. D. Romik. The number of steps in the Robinson-Schensted algorithm. Functional Analysis and Its Applications, vol. 39, pp. 152-155, 2005.
  35. G. Kindler and D. Romik. On distributions computable by random walks on graphs. SIAM Journal on Discrete Mathematics, vol. 17, pp. 624-633, 2004.
  36. A. Holroyd, T. Liggett, and D. Romik. Integrals, partitions and cellular automata. Transactions of the American Mathematical Society, vol. 356, pp. 3349-3368, 2004.
  37. D. Romik. Partitions of n into t √n parts. European Journal of Combinatorics, vol. 26, pp. 1-17, 2005.
  38. D. Romik. Explicit formulas for hook walks on continual Young diagrams. Advances in Applied Mathematics, vol. 32, pp. 625-654, 2004.
  39. A. Naor and D. Romik. Projecting the surface measure of the sphere of l_p^n. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, vol. 39, pp. 241-261, 2003.
  40. D. Romik. Some comments on Euler's series for π²/6. Mathematical Gazette, July 2002, pp. 281-284.
  41. D. Romik. Stirling's approximation for n!: the ultimate short proof? American Mathematical Monthly, vol. 107, pp. 556-557, 2000.
  42. D. Romik. Sharp entropy bounds for discrete statistical simulation. Statistics & Probability Letters, vol. 42, pp. 219-227, 1999.

Conference proceedings

  1. D. Romik. Local extrema in random permutations and the structure of longest alternating subsequences. Discrete Mathematics and Theoretical Computer Science, Proceedings Vol. AO, pp. 825-834, 2011. (FPSAC 2011)
  2. E. Bisi, F. D. Cunden, S. Gibbons, and D. Romik. Sorting networks, staircase Young tableaux and last passage percolation. Séminaire Lotharingien de Combinatoire, vol. 84B.3, 12 pp, 2020. (FPSAC 2020)

Patents

  1. Y. Baryshnikov, D. Romik, E. H. Grosse, and F. X. Zane. Method and apparatus for filtering data packets. United States Patent 8,355,324.