Publications and Preprints

My papers can be found on my publications page, as well as on the arXiv and Google Scholar.

Publications

  • The Exact Rank of Sparse Random Graphs
    Margalit Glasgow, Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Journal of the European Mathematical Society, to appear arXiv:2303.05435

  • The limiting spectral law for sparse iid matrices
    Ashwin Sah, Julian Sahasrabudhe and Mehtaab Sawhney. Forum of Mathematics, Pi, to appear arXiv:2310.17635

  • The existence of subspace designs
    Peter Keevash, Ashwin Sah and Mehtaab Sawhney. Proceedings of the London Mathematical Society, to appear arXiv:2212.00870

  • An explicit economical additive basis
    Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney and Dmitrii Zakharov. Combinatorics, Computing and Probability, to appear arXiv:2405.08650

  • Effective bounds for Roth's theorem with shifted square common difference
    Sarah Peluse, Ashwin Sah and Mehtaab Sawhney. American Journal of Mathematics, to appear arXiv:2309.08359

  • A central limit theorem for the matching number of a sparse random graph
    Margalit Glasgow, Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Journal of the London Mathematical Society, to appear arXiv:2402.05851

  • On the Spielman-Teng Conjecture
    Ashwin Sah, Julian Sahasrabudhe and Mehtaab Sawhney. Geometric and Functional Analysis, to appear arXiv:2405.20308

  • Vinogradov's theorem for primes with restricted digits
    James Leng and Mehtaab Sawhney. IMRN, to appear arXiv:2409.06894

  • The sparse circular law, revisited
    Ashwin Sah, Julian Sahasrabudhe and Mehtaab Sawhney. Bulletin of London Mathematical Society, to appear arXiv:2310.17600

  • Improved bounds for five-term arithmetic progressions
    James Leng, Ashwin Sah and Mehtaab Sawhney. Mathematical Proceedings of the Cambridge Philosophical Society, to appear arXiv:2312.10776

  • High-Girth Steiner Triple Systems
    Matthew Kwan, Ashwin Sah, Mehtaab Sawhney and Michael Simkin. Annals of Mathematics, (2) 200(3): 1059-1156 (November 2024). arXiv:2201.04554

  • On Perfectly Friendly Bisections of Random Graphs
    Dor Minzer, Ashwin Sah and Mehtaab Sawhney. Annals of Probability, 2024, Vol. 52, No. 6, 2281-2341. arXiv:2305.03543

  • The intransitive dice kernel: \(\frac{\mathbf{1}_{x\ge y}-\mathbf{1}_{x\le y}}{4} - \frac{3(x-y)(1+xy)}{8}\)
    Ashwin Sah and Mehtaab Sawhney. Probability Theory and Related Fields, 2024, Volume 189, pages 1073–1128. arXiv:2302.11293

  • Distribution of the threshold for the symmetric perceptron
    Ashwin Sah and Mehtaab Sawhney. FOCS 2023 arXiv:2301.10701

  • Anticoncentration in Ramsey graphs and a proof of the Erdős-McKay conjecture
    Matthew Kwan, Ashwin Sah, Lisa Sauermann and Mehtaab Sawhney. Forum of Mathematics, Pi, (2023) Vol. 11:e21 1–74 arXiv:2208.02874

  • Subgraph distributions in dense random regular graphs
    Ashwin Sah and Mehtaab Sawhney. Compositio Mathematica, 159 (2023) 2125--2148 arXiv:2209.00734

  • Paths of given length in tournaments
    Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Combinatorial Theory, 3 (2)(2023), #5. arXiv:2012.00262

  • Cayley graphs that have a quantum ergodic eigenbasis
    Assaf Naor, Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Israel Journal of Mathematics, 256 (2023), 599--617 arXiv:2207.05527

  • Threshold for Steiner triple systems
    Ashwin Sah, Mehtaab Sawhney and Michael Simkin. Geometric and Functional Analysis, 33(4) (2023), 1141--1172 arXiv:2204.03964

  • Optimal minimization of the covariance loss
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. IEEE Transactions in Information Theory, 69(2) (2023), 813--818 arXiv:2205.01773

  • Spencer's theorem in nearly-input sparsity time
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. SODA 2023 arXiv:2206.04549

  • Friendly bisections of random graphs
    Asaf Ferber, Matthew Kwan, Bharghav Narayanan, Ashwin Sah and Mehtaab Sawhney. Communications of the American Mathematical Society, 2 (2022), 380--416 arXiv:2105.13337

  • Enumerating Matroids and Linear Spaces
    Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Comptes Rendus Mathématique, 361 (2023), 565--575 arXiv:2112.03788

  • Sparse recovery properties of discrete random matrices
    Asaf Ferber, Ashwin Sah, Mehtaab Sawhney and Yizhe Zhu. Combinatorics, Probability and Computing, 32(2) (2023), 316--325 arXiv:2203.06115

  • Substructures in Latin squares
    Matthew Kwan, Ashwin Sah, Mehtaab Sawhney and Michael Simkin. Israel Journal of Mathematics, 256 (2023), 363--416 arXiv:2202.05088

  • Enumerating coprime permutations
    Ashwin Sah and Mehtaab Sawhney. Mathematika, 68(4) (2023), 1120-1134 arXiv:2203.06268

  • Singularity of the \(k\)-core of a random graph
    Asaf Ferber, Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Duke Mathematical Journal, 172(7) (2023), 1293--1332 arXiv:2106.05719

  • Random symmetric matrices: rank distribution and irreducibility of the characteristic polynomial
    Asaf Ferber, Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Mathematical Proceedings of the Cambridge Philosophical Society, 174(2) (2023), 233-246 arXiv:2106.04049

  • Majority Dynamics: The Power of One
    Ashwin Sah and Mehtaab Sawhney. Israel Journal of Mathematics, to appear arXiv:2105.13301

  • Rank deficiency of random matrices
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Electronic Communications in Probability, 27 (2022), 1-9. arXiv:2103.02467

  • Fast and memory optimal dimension reduction using Kac's walk.
    Vishesh Jain, Natesh Pillai, Ashwin Sah, Mehtaab Sawhney and Aaron Smith. Annals of Applied Probability, 32(5) (2022), 4038-4064. arXiv:2003.10069

  • Online Edge Coloring via Tree Recurrences and Correlation Decay
    Janardhan Kulkarni, Yang Liu, Ashwin Sah, Mehtaab Sawhney and Jakub Tarnawski. STOC 2022 arXiv:2111.00721

  • Approximate counting and sampling via local central limit theorems
    Vishesh Jain, Will Perkins, Ashwin Sah and Mehtaab Sawhney. STOC 2022 arXiv:2108.01161

  • Optimal and algorithmic norm regularization of random matrices
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Proceedings of the American Mathematical Society, 150(10) (2022), 4503-4518. arXiv:2012.00175

  • Large deviations in random Latin squares
    Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Bulletin of the London Mathematical Society, 54(4) (2022), 1420-1438. arXiv:2106.11932

  • A Gaussian fixed point random walk
    Yang Liu, Ashwin Sah and Mehtaab Sawhney. ITCS 2022 arXiv:2104.07009

  • Non-classical polynomials and the inverse theorem
    Aaron Berger, Ashwin Sah, Mehtaab Sawhney and Jonathan Tidor. Mathematical Proceedings of the Cambridge Philosophical Society, 173(3) (2022), 525-537. arXiv:2107.07495

  • Popular differences for matrix patterns
    Aaron Berger, Ashwin Sah, Mehtaab Sawhney and Jonathan Tidor. Transactions of the American Mathematical Society, 375(4) (2022), 2677-2704. arXiv:2102.01684

  • On the smallest singular value of symmetric random matrices
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Combinatorics, Probability and Computing, 31(4) (2022), 662-683. arXiv:2011.02344

  • Singularity of discrete random matrices
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Geometric and Functional Analysis, 31(5) (2021), 1160-1218. arXiv:2010.06554

  • The smallest singular value of dense random regular digraphs.
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. IMRN, 24 (2022), 19300--19334. arXiv:2008.04755

  • The cylindrical width of transitive sets
    Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Israel Journal of Mathematics, 253 (2) (2023), 647--672. arXiv:2101.11207

  • Local limit theorems for subgraph counts.
    Ashwin Sah and Mehtaab Sawhney. Journal of the London Mathematical Society, 105(2) (2022), 950-1011. arXiv:2006.11369

  • On the smoothed analysis of the smallest singular value with discrete noise
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Bulletin of the London Mathematical Society, 54(2) (2022), 369-388. arXiv:2009.01699

  • Patterns without a popular difference.
    Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Discrete Analysis, 2021:8. arXiv:2004.07722

  • Anticoncentration versus the number of subset sums
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Advances in Combinatorics, 2021:6. arXiv:2101.07726

  • On the real Davies' conjecture.
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Annals of Probability, 49(6) (2021), 3011-3031. arXiv:2005.08908

  • Perfectly Sampling \(k\ge(8/3+o(1))\Delta\)-Colorings in Colors.
    Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. STOC 2021 arXiv:2007.06360

  • Discrepancy Minimization via a Self-Balancing Walk.
    Ryan Alweiss, Yang Liu and Mehtaab Sawhney. STOC 2021 arXiv:2006.14009

  • A counterexample to the Bollobás-Riordan conjectures on sparse graph limits.
    Jonathan Tidor, Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Combinatorics, Probability and Computing, 30(5) (2021), 796-799. arXiv:2003.05272

  • Cayley graphs without a bounded eigenbasis.
    Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. IMRN, 2022(8), 6157-6185. arXiv:2005.04502

  • Number of arithmetic progressions in dense random subsets of \(\mathbb{Z}/n\mathbb{Z}\).
    Ross Berkowitz, Ashwin Sah and Mehtaab Sawhney. Israel Journal of Mathematics, 244 (2021), 589-620. arXiv:1907.11807

  • Bounded Degree Spanners of the Hypercube.
    Rajko Nenadov, Mehtaab Sawhney, Benny Sudakov and Adam Wagner. Electronic Journal of Combinatorics, 27 (2020), P3.3. arXiv:1910.09868

  • Exponential improvements for superball packing upper bounds.
    Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. Advances in Mathematics, 365 (2020), 107056. arXiv:1904.11462

  • Triforce and Corners.
    Jacob Fox, Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. Mathematical Proceedings of the Cambridge Philosophical Society, 169 (2020), 209–223. arXiv:1903.04863

  • A reverse Sidorenko inequality.
    Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. Inventiones Mathematicae, 221 (2020), 665–711. arXiv:1809.09462

  • The number of independent sets in an irregular graph.
    Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. Journal of Combinatorial Theory, Series B, 138 (2019), 172-195. arXiv:1805.04021

  • Hypercube Packings and Coverings with Higher Dimensional Rooks.
    Mehtaab Sawhney and David Stoner. Australasian Journal of Combinatorics, 77 (2020), 9--34. arXiv:1801.10607

  • Properties of non-symmetric Macdonald polynomials at \(q = 1\) and \(q = 0\).
    Per Alexandersson and Mehtaab Sawhney. Annals of Combinatorics, 23, No.2, 219--239 (2019). arXiv:1801.04550

  • On the Discrepancy Between Two Zagreb Indices.
    Ashwin Sah and Mehtaab Sawhney. Discrete Mathematics, 341 (2018), 2575--2589. arXiv:1801.02532

  • Characters of Independent Stanley Sequences.
    Richard Moy, Mehtaab Sawhney and David Stoner. European Journal of Combinatorics, 70 (2018), 354--363. arXiv:1708.01849

  • On a conjecture regarding permutations which destroy arithmetic progressions
    Mehtaab Sawhney and David Stoner. Electronic Journal of Combinatorics, 25 (2018), P2.42. arXiv:1708.00144

  • On Symmetric But Not Cyclotomic Numerical Semigroups
    Mehtaab Sawhney and David Stoner. SIAM Journal of Discrete Mathematics, 32 (2018), 1296--1304. arXiv:1707.00782

  • A major-index preserving map on fillings.
    Per Alexandersson and Mehtaab Sawhney. Electronic Journal of Combinatorics, 24, No.4, 2017. arXiv:1703.03088

  • Further Results on Bar and Arc \(k-\)Visibility Graph.
    Mehtaab Sawhney and Jonathan Weed. Minnesota Journal of Undergraduate Mathematics, Volume 3 (2018). arXiv:1601.01231

  • Two classes of modular \(p-\)Stanley sequences.
    Mehtaab Sawhney and Jonathan Tidor. Journal of Combinatorics, 11 (2020), 127--140 arXiv:1506.07941

    • Preprints

    • On polynomial progressions via transference
      Daniel Altman and Mehtaab Sawhney Submitted arXiv:2506.13010

    • Quasipolynomial bounds for the corners theorem
      Michael Jaber, Yang P. Liu, Shachar Lovett, Anthony Ostuni and Mehtaab Sawhney Submitted arXiv:2504.07006

    • The random graph process is globally synchronizing
      Vishesh Jain, Clayton Mizgerd and Mehtaab Sawhney. Submitted arXiv:2501.12205

    • Local limit theorem for joint subgraph counts
      Ashwin Sah, Mehtaab Sawhney and Daniel G. Zhu. Submitted arXiv:2412.09535

    • New bounds for the Furstenberg-Sárközy Theorem
      Ben Green and Mehtaab Sawhney. Submitted arXiv:2411.17448

    • Hitting time mixing for the random transposition walk
      Vishesh Jain and Mehtaab Sawhney. Submitted arXiv:2410.23944

    • Primes of the form \(p^2 + nq^2\)
      Ben Green and Mehtaab Sawhney. Submitted arXiv:2410.04189

    • Free Energy Universality of Spherical Spin Glasses
      Mehtaab Sawhney and Mark Sellke. Submitted arXiv:2408.13701

    • On further questions regarding unit fractions
      Yang P. Liu and Mehtaab Sawhney. Submitted arXiv:2404.07113

    • Improved Bounds for Szemerédi's Theorem
      James Leng, Ashwin Sah and Mehtaab Sawhney. Submitted arXiv:2402.17995

    • Quasipolynomial bounds on the inverse theorem for the Gowers \(U^{s+1}[N]\)-norm
      James Leng, Ashwin Sah and Mehtaab Sawhney. Submitted arXiv:2402.17994

    • A Toolkit for Robust Thresholds
      Huy Tuan Pham, Ashwin Sah, Mehtaab Sawhney and Michael Simkin. Submitted arXiv:2210.03064