Research papers
of Pietro Caputo

1. PC, Matteo Quattropani, Federico Sau
   A universal cutoff phenomenon for mean-field exchange models. arXiv:2506.12816


2. PC, Zongchen Chen, Daniel Parisi
   Factorizations of relative entropy using stochastic localization arXiv:2503.19419


3. PC, Zongchen Chen, Yuzhou Gu, Yury Polyanskiy
   Entropy Contractions in Markov Chains: Half-Step, Full-Step and Continuous-Time. arXiv:2409.07689


4. PC, Matteo Quattropani, Federico Sau
   Repeated Block Averages: entropic time and mixing profiles. arXiv:2407.16656


5. PC, Justin Salez,
   Entropy factorization via curvature. arXiv:2407.13457


6. PC, Sebastien Ott, Assaf Shapira,
   Relaxation time and topology in 1D O(N) models. arXiv:2407.12610


7. PC, Cyril Labbe', Hubert Lacoin,
   Cutoff phenomenon in nonlinear recombinations. The Annals of Applied Probability, 2025. arXiv:2402.11396


8. PC, Florentin Münch, Justin Salez,
   Entropy and curvature: beyond the Peres-Tetali conjecture. Transactions of the American Mathematical Society, 2025. arXiv:2401.17148


9. Mriganka Basu Roy Chowdhury, PC, Shirshendu Ganguly,
   Characterizing Gibbs states for area-tilted Brownian lines. The Annals of Probability, 2025. arXiv:2310.06817


10. PC, Alistair Sincalir
    Nonlinear dynamics for the Ising model. Communications in Mathematical Physics 405, 2024 (open access).
    Preliminary version appears in STOC24. arXiv:2305.18788


11. PC, Shirshendu Ganguly,
    Uniqueness, mixing, and optimal tails for Brownian line ensembles with geometric area tilt.
    Probability and Mathematical Physics 6, 2025. arXiv:2305.18280


12. PC, Matteo Quattropani, Federico Sau
    Cutoff for the Averaging process on the hypercube and complete bipartite graphs arXiv:2212.08870
    Electronic Journal of Probability 28 , 2023


13. PC, Daniel Parisi,
    Nonlinear recombinations and generalized random transpositions arXiv:2207.04775
    Annales Henri Lebesgue 7 , 2024


14. PC, Lecture notes on entropy and Markov chains pdf file (Fall 2022)


15. Alexandre Bristiel, PC,
    Entropy inequalities for random walks and permutations arXiv:2109.06009
    Annales de l'IHP 60, 2024


16. Xing Shi Cai, PC, Guillem Perarnau, Matteo Quattropani
    Rankings in directed configuration models with heavy tailed in-degrees arXiv:2104.08389
    Annals of Applied Probability 33 , 2023


17. Antonio Blanca, PC, Zongchen Chen, Daniel Parisi, Daniel Stefankovic, Eric Vigoda,
    On Mixing of Markov Chains: Coupling, Spectral Independence, and Entropy Factorization.
    Electronic Journal of Probability 27 , 2022. (Conference version appears in SODA 2022) arXiv:2103.07459


18. David Aldous, PC, Rick Durrett, Alexander E. Holroyd, Paul Jung, Amber L. Puha,
    The Life and Mathematical Legacy of Thomas M. Liggett
    Notices of the American Mathematical Society 68 , 2021. arXiv:2008.03137


19. PC, Cyril Labbe', Hubert Lacoin,
    Spectral gap and cutoff phenomenon for the Gibbs sampler of $\nabla\varphi$ interfaces with convex potential.
    Annales de l'IHP 58, 2022. arXiv:2007.10108


20. Antonio Blanca, PC, Daniel Parisi, Alistair Sinclair, Eric Vigoda,
    Entropy decay in the Swendsen-Wang dynamics. arXiv:2007.06931
    Annals of Applied Probability 32, 2022. (Preliminary version appers in STOC 2021)


21. PC, Daniel Parisi,
    Block factorization of the relative entropy via spatial mixing
    Communications in Mathematical Physics 388, 2021. (open access) arXiv:2004.10574


22. PC, Matteo Quattropani,
    Mixing time trichotomy in regenerating dynamic digraphs
    Stochastic Processes and Applications 137, 2021 arXiv:1911.07025


23. PC, Matteo Quattropani,
    Stationary distribution and cover time of sparse directed configuration models.
    Probability Theory and Related Fields 178, 2020 (open access) arXiv:1909.05752


24. PC, Matteo Quattropani,
    Mixing time of PageRank surfers on sparse random digraphs
    Random Structures and Algorithms 59, 376-406, 2021. arXiv:1905.04993


25. PC, Cyril Labbe', Hubert Lacoin,
    Mixing time of the adjacent walk on the simplex,
    Annals of Probability 48, 2020. arXiv:1904.01088


26. PC, Dima Ioffe, Vitali Wachtel,
    Tightness and line ensembles for Brownian Polymers under Geometric Area Tilts ,
    In: Statistical Mechanics of Classical and Disordered Systems (pp. 241-266) 2019, Springer. arXiv:1906.06533


27. PC, Dima Ioffe, Vitali Wachtel,
    Confinement of Brownian Polymers under Geometric Area Tilts
    Electronic Journal of Probability 24, 2019 arXiv:1809.03209


28. Antonio Blanca, PC, Alistair Sinclair, Eric Vigoda,
    Spatial mixing and non-local Markov chains
    Random Structures & Algorithms 55 , 584-614, 2019. arXiv:1708.01513 (Conference version: SODA 2017)


29. PC, Fabio Martinelli and Fabio Lucio Toninelli,
    Entropic repulsion in $|\nabla\phi|^p$ surfaces: a large deviation bound for all $p\ge 1$.
    Boll. Unione Mat. Ital. 10 , 2017. arXiv:1701.03327


30. Charles Bordenave, PC, Justin Salez,
    Cutoff at the 'entropic time' for sparse Markov chains
    Probability Theory and Related Fields 173, 2019 arXiv:1611.01079


31. PC, Alistair Sinclair
    Entropy production in nonlinear recombination models
    Bernoulli Journal 24, 3246-3282, 2018 arXiv:1609.06897


32. Charles Bordenave, PC, Djalil Chafai, Konstantin Tikhomirov
    On the spectral radius of a random matrix: an upper bound without fourth moment
    Annals of Probability 46 , 2018 arXiv:1607.05484


33. Charles Bordenave, PC, Justin Salez,
    Random walk on sparse random digraphs.
    Probability Theory and Related Fields 170 6, 933-960, 2018 arXiv:1508.06600


34. Charles Bordenave, PC and Djalil Chafai, Daniele Piras
    Spectrum of large random Markov chains: Heavy-tailed weights on the oriented complete graph,
    Random Matrices Theory Appl. 6 , no. 2, 2017. arXiv:1610.01836


35. PC, Fabio Martinelli, Alistair Sinclair, Alexandre Stauffer,
    Dynamics of Lattice Triangulations on Thin Rectangles.
    Electronic J. Probability 21, 2016 arXiv:1505.06161


36. PC, Julien Sohier,
    Convergence to equilibrium for a directed (1+d)-dimensional polymer.
    Ann. Fac. Sci. Toulouse Math. 26, 2017 (special issue in honor of D. Bakry) arXiv:1504.02354


37. PC, Fabio Martinelli and Fabio Lucio Toninelli,
    Multi-level pinning problems for random walks and self-avoiding lattice paths.
    Electronic Journal of Probability 20, no. 8, 1-29, 2015 arXiv:1410.2694


38. PC, Fabio Martinelli and Fabio Lucio Toninelli,
    On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature.
    Probability Theorey and Related Fields 163, no. 3-4, 803-831, 2015 arXiv:1406.1206


39. PC, Georg Menz, Prasad Tetali,
    Approximate tensorization of entropy at high temperature.
    Ann. Fac. Sci. Toulouse 24, no. 4, 691-716, 2015 (special issue in honor of P. Diaconis) arXiv:1405.0608


40. Charles Bordenave, PC
    Large deviations of empirical neighborhood distribution in sparse random graphs.
    Probability Theory and Related Fields 163, no. 1-2, 149-222, 2015. arXiv:1308.5725


41. PC, Eyal Lubetzky, Fabio Martinelli, Allan Sly, Fabio Lucio Toninelli,
    Scaling limit and cube-root fluctuations in SOS surfaces above a wall
    J. Eur. Math. Soc. (JEMS) 18 , 2016. arXiv:1302.6941


42. PC, Fabio Martinelli, Alistair Sinclair, Alexandre Stauffer,
    Random Lattice Triangulations: Structure and Algorithms ,
    Annals of Applied Probability 163, no. 3-4, 803-831, 2015, arXiv:1211.1784 (Conference version appears in STOC 2013)


43. Charles Bordenave, PC, Large deviation principle for Wigner matrices without gaussian tails
    Annals of Probability 42, no. 6, 2454-2496, 2014 arXiv:1207.5570


44. Charles Bordenave, PC and Djalil Chafai,
    Spectrum of Markov generators on sparse random graphs, Communications in Pure and Applied Math. 67 , 621-669, 2014. arXiv:1202.0644


45. PC, E. Lubetzky, F. Martinelli, A. Sly, and F.L. Toninelli,
    Dynamics of 2+1 dimensional SOS surfaces above a wall: slow mixing induced by entropic repulsion,
    Annals of Probability 42, no. 4, 1516-1589, 2014. arXiv:1205.6884


46. PC, E. Lubetzky, F. Martinelli, A. Sly, and F.L. Toninelli,
    The shape of the (2+1)D SOS surface above a wall, C. R. Math. Acad. Sci. Paris 350, no. 13-14, 703-706, 2012.


47. PC, Hubert Lacoin, Fabio Martinelli, Francois Simenhaus, Fabio Lucio Toninelli,
    Polymer dynamics in the depinned phase: metastability with logarithmic barriers,
    Probability Theory and Related Fields 153, 587-641, 2012 arXiv:1007.4470


48. PC, F. Martinelli, and F.L. Toninelli,
    Mixing times of monotone surfaces and SOS interfaces: a mean curvature approach, Communications in Mathematical Physics 311 , 157- 189, 2012 arXiv:1101.4190


49. PC, Fabio Martinelli, Francois Simenhaus, Fabio Lucio Toninelli,
    "Zero" temperature stochastic 3D Ising model and dimer covering fluctuations: a first step towards interface mean curvature motion,
    Communications in Pure and Applied Math 64, 778-831, 2011, arXiv:1007.3599


50. PC, F. Martinelli, and F.L. Toninelli, Sharp mixing times for sampling random surfaces
    Proceedings of IEEE FOCS 2011.


51. Charles Bordenave, PC and Djalil Chafai,
    Spectrum of non-Hermitian heavy tailed random matrices
    Communications in Mathematical Physics 307, 513-560, 2011, arXiv:1006.1713


52. PC, Alessandra Faggionato and Timothy Prescott,
    Invariance principle for Mott variable range hopping and other walks on point processes,
    Annales de l'Institut Henri Poincare Probab. et Stat. 49 , 654-697, 2013 arXiv:0912.4591


53. PC, Thomas M. Liggett and Thomas Richthammer,
    Proof of Aldous' spectral gap conjecture,
    Journal of the American Mathematical Society 23 , 831-851, 2010 arXiv: 0906.1238


54. PC, Fabio Martinelli and Fabio Lucio Toninelli,
    Convergence to equilibrium of biased plane partitions,
    Random Structures & Algorithms 39 , 83-114, 2011, arXiv: 0903.5079


55. Charles Bordenave, PC and Djalil Chafai,
    Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph,
    Annals of Probability 39, 1544-1590, 2011 arXiv:0903.3528


56. PC, Alessandra Faggionato and Alexandre Gaudilliere,
    Recurrence and transience for long-range reversible random walks on a random point process,
    Electron. J. Probab. 14, 2580-2616, 2009 arxiv:0811.4623


57. Charles Bordenave, PC and Djalil Chafai,
    Spectrum of large random reversible Markov chains: two examples.
    ALEA, Latin American Journal Of Probability And Mathematical Statistics 6 , 2010 arXiv:0811.1097


58. Charles Bordenave, PC and Djalil Chafai,
    Circular law theorem for random Markov matrices.
    Probability Theory and Related Fields 152, 751-779, 2012, arXiv:0808.1502


59. PC and Alessandra Faggionato,
    Diffusivity in one-dimensional generalized Mott variable-range hopping models,
    Annals of Applied Probability 10, 1459-1494, 2009 arxiv math.PR/0701253


60. PC, On the spectral gap of the Kac walk and other binary collision processes,
    ALEA, Latin American Journal Of Probability And Mathematical Statistics 4 , 205-222, 2008 arXiv:0807.3415


61. PC, Paolo Dai Pra, Gustavo Posta,
    Convex entropy decay via the Bochner--Bakry--Emery approach,
    Annales de l'Institut Henri Poincare Probab. et Stat. 45, 734-753, 2009 arXiv:0712.2578


62. PC, Fabio Martinelli and Fabio Lucio Toninelli,
    On the approach to equilibrium for a polymer with adsorption and repulsion ,
    Electron. J. Probab. 13, 213-258, 2008 arXiv:0709.2612


63. PC and Alessandra Faggionato,
    Isoperimetric inequalities and mixing time for a random walk on a random point process ,
    Annals of Applied Probability 17, 1707-1744, 2007 arxiv math.PR/0607805


64. Nayantara Bhatnagar, PC, Prasad Tetali, Eric Vigoda,
    Analysis of Top-Swap Shuffling for Genome Rearrangements,
    Annals of Applied Probability 17, 1424-1445, 2007 arxiv math.PR/0609171


65. PC and G. Posta,
    Entropy dissipation estimates in a zero-range dynamics,
    Probab. Theory and Rel. Fields 139, 65-87, 2007 pdf-file


66. A.S. Boudou, PC, P. Dai Pra, G. Posta,
    Spectral gap inequalities for interacting particle systems via a Bochner type inequality ,
    J. Funct. Anal. 232 , 222-258, 2006. pdf-file


67. N. Cancrini, PC and F. Martinelli,
    Relaxation time for L-reversal processes and other chormosome shuffles ,
    Annals of Appl. Probab. 16, 1506-1527, 2006 pdf-file


68. PC and F. Martinelli,
    Phase ordering after a deep quench: The stochastic Ising and hard--core gas models on a tree ,
    Probab. Theory and Rel. Fields, 136, 37-80, 2006 pdf-file


69. PC, Energy gap estimates in XXZ ferromagnets and stochastic particle systems
    Markov Process. Related Fields 11, 189--210, 2005 pdf-file


70. PC, Spectral gap inequalities in product spaces with conservation laws, in:
    T. Funaki and H. Osada (eds.) Adv. Studies in Pure Math. Japan 2004 ps-file


71. PC, Uniform Poincare inequalities for unbounded conservative spin systems: The non-interacting case,
    Stoch. Proc. Appl. 106, No. 2, 223--244, 2003. ps-file


72. PC and F. Martinelli,
    Relaxation time of anisotropic simple exclusion processes and quantum Heisenberg models,
    Ann. Appl. Probab. 13 , No. 2, 691--721, 2003. gzipped ps-file


73. PC and D. Ioffe,
    Finite volume approximation of the effective diffusion matrix: The case of independent bond disorder,
    Ann. Inst. H. Poincare (Probab. et Stat.) 39 , No.\ 3, 505--525, 2003. ps-file


74. PC and F. Martinelli,
    Asymmetric diffusion and the enrgy gap above the 111 ground state of the quantum XXZ model ,
    Commun. Math. Phys. 226 , 323 - 375, 2002. gzipped ps-file


75. PC, A remark on spectral gap and logarithmic Sobolev inequalities for conservative spin systems,
    2001, Unpublished. ps-file


76. PC and J.-D. Deuschel,
    Critical large deviations in harmonic crystals with long range interactions,
    Ann. Probab. 29 , 2001. gzipped ps-file


77. PC and Y. Velenik,
    A note on wetting transition for gradient fields,
    Stoch. Proc. Appl. 87 , 107-113, 2000. ps-file


78. PC and J-D. Deuschel,
    Large deviations and variational principle for harmonic crystals ,
    Commun. Math. Phys. 209 , 595-632, 2000. gzipped ps-file


79. PC, Harmonic Crystals: Statistical Mechanics and Large Deviations,
    PhD Thesis, Berlin Jan. 2000 gzipped ps-file