Preprints:
Disorder chaos in short-range, diluted, and Lévy spin glasses (with H. Kim and A. Sen)
A Gaussian convexity for logarithmic moment generating functions
Some rigorous results on the Levy spin glass model (with H. Kim and A. Sen)
Performance of Bayesian linear regression in a model with mismatch (with J. Barbier, D. Panchenko, M. Saénz)
Publications:
On the TAP equations via the cavity approach in the generic mixed p-spin models (with S. Tang) Comm. Math. Phys., Vol. 405, No. 87 (2024)
Universality of superconcentration in the Sherrington-Kirkpatrick model (with W.-K. Lam) Random Structures Algorithms, Vol. 64, No. 2, 267-286 (2024)
The generalized TAP free energy (with D. Panchenko and E. Subag) Comm. Pure Appl. Math., Vol. 76, No. 7, 1329-1415 (2023)
Free energy of a diluted spin glass model with quadratic Hamiltonian (with R. Biswas and A. Sen) Ann. Probab. Vol. 51, No 1, 359-395 (2023)
On ℓp-Gaussian-Grothendieck problem (with A. Sen) Int. Math. Res. Not., Vol. 2023, No. 3, 2344-2428 (2023)
On the Almeida-Thouless transition line in the SK model with centered Gaussian external field Electron. Commun. Probab. Vol. 26, No. 65, 1-9 (2021)
Phase transition in random tensors with multiple spikes (with M. Handschy and G. Lerman) Ann. App. Probab. Vol. 31, No. 4, 1868-1913 (2021)
On convergence of the cavity and Bolthausen's TAP iterations to the local magnetization (with S. Tang) Comm. Math. Phys. Vol. 386, No 2, 1209-1242 (2021)
Universality of Approximate Message Passing algorithms (with W.-K. Lam) Electron. J. Probab, Vol. 26, No. 36, 1-44 (2021)
The generalized TAP free energy II (with D. Panchenko and E. Subag) Comm. Math. Phys., Vol. 381, 257-291 (2021)
The SK model is infinite step replica symmetry breaking at zero temperature (with A. Auffinger and Q. Zeng) Comm. Pure Appl. Math., Vol. 73, No. 5 (2020)
Order of fluctuations of the free energy in the SK model at critical temperature (with W.-K. Lam) ALEA, Vol. XVI, 809-916 (2019)
Phase transition in the spiked random tensor with Rademacher prior Ann. Statist., Vol.47, No. 5, 2734-2756 (2019)
Suboptimality of local algorithms for a class of max-cut problems (with D. Gamarnik, D. Panchenko, M. Rahman) Ann. Probab.,Vol. 47, No. 3, 1587-1618 (2019)
On the TAP free energy in the mixed p-spin models (with D. Panchenko) Comm. Math. Phys., Vol. 362, No. 1, 219-252 (2018)
Disorder chaos in some diluted spin glass models (with D. Panchenko) Ann. App. Probab., Vol. 28, No. 3, 1356–1378 (2018)
On the energy landscape of spherical spin glasses (with A. Auffinger) Adv. Math., Vol. 330, 553-588 (2018)
On concentration properties of disordered Hamiltonians (with A. Auffinger) Proc. Amer. Math. Soc., Vol. 146, 1807-1815 (2018)
On the energy landscape of the mixed even p-spin model (with M. Handschy and G. Lerman) Probab. Theory Related Fields., Vol. 171, No. 1-2, 53-95 (2018)
Parisi formula for the ground state energy in the mixed p-spin model (with. A. Auffinger) Ann. Probab., Vol. 45, No. 6B, 4617-4631 (2017)
Variational representations for the Parisi functional and the two-dimensional Guerra-Talagrand bound Ann. Probab., Vol. 45, No. 6A, 3929-3966 (2017)
A duality principle in spin glasses (with A. Auffinger) Electron. J. Probab., Vol 22, No. 61 (2017)
Fluctuations of the free energy in the mixed p-spin models with external field (with P. Dey and D. Panchenko) Probab. Theory Related Fields. Vol 168, No. 1, 41-53 (2017)
Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed p-spin models (with A. Sen) Comm. Math. Phys., Vol 350, No. 1, 129-173 (2017)
Temperature chaos in some spherical mixed p-spin models (with D. Panchenko) J. Stat. Phys., Vol 166, No. 5, 1151-1162 (2017)
Some examples of quenched self-avaraging in models with Gaussian disorder (with D. Panchenko) Ann. Inst. Henri Poincaré Probab. Stat., Vol 53, No. 1, 243-258 (2017)
The Legendre structure of the Parisi formula (with A. Auffinger) Comm. Math. Phys., Vol 348, No. 3, 751–770 (2016)
Limit Theorems in the Imitative Monomer-Dimer Mean-Field Model via Stein's Method J. Math. Phys., Vol 57, 083302 (2016)
Universality of chaos and ultrametricity in mixed p-spin models (with A. Auffinger) Comm. Pure Appl. Math., Vol. 69, No. 11, 2107-2130 (2016)
Improved Hölder and reverse Hölder inequalities for Gaussian random vectors (with N. Dafnis and G. Paouris) Adv. Math., Vol. 280, 643-689 (2015)
Disorder chaos in the spherical mean field model (with H.-W. Hsieh, C.-R. Hwang, and Y.-C. Sheu) J. Stat. Phys., Vol. 160, No. 2, 417-429 (2015)
The Parisi formula has a unique minimizer (with A. Auffinger) Comm. Math. Phys., Vol. 335, No. 3, 1429-1444 (2015)
Partial results on the convexity of the Parisi functional with PDE approach Proc. Amer. Math. Soc., Vol. 143, 3135-3146 (2015)
On properties of Parisi measures (with A. Auffinger) Probab. Theory Related Fields, Vol. 161, No. 3, 817-850 (2015)
Free energy and complexity of spherical bipartite models (with A. Auffinger) J. Stat. Phys., Vol. 157, No. 1, 40-59 (2014)
Chaos in the mixed even-spin models Comm. Math. Phys., Vol. 328, No. 3, 867-901 (2014)
On the mixed even-spin Sherrington-Kirkpatrick model with ferromagnetic interaction Ann. Inst. Henri Poincaré Probab. Stat., Vol. 50, No. 1, 63-83 (2014)
The Aizenman-Sims-Starr scheme and Parisi formula for mixed p-spin spherical models Electron. J. Probab., Vol. 18, No. 94, 1-14 (2013)
An approach to chaos in some mixed p-spin models (with D. Panchenko) Probab. Theory Related Fields, Vol. 151, No. 1, 389-404 (2013)
Disorder chaos in the Sherrington-Kirkpatrick model with external field Ann. Probab., Vol. 41, No. 5, 3345-3391 (2013)
Central limit theorems for cavity and local fields of the Sherrington-Kirkpatrick model Electron. J. Probab., Vol. 18, No. 2, 1-25 (2013)
On the optimal transition matrix for MCMC sampling (with T.-L. Chen, C.-R. Hwang, and H.-M. Pai) SIAM J. Control Optim., Vol. 50, No. 5, 2743-2762 (2012)