Projects
Research Interests

Research Interests

$\bullet$ Large deviations, interacting Brownian motions, applications to models in quantum statistical mechanics (e.g. Fröhlich Polaron, Bose-Einstein condesation, Gross-Pitaevskii formula)
$\bullet$ Stochastic PDEs, directed polymers, Gaussian multiplicative chaos, Gaussian free fields and Liouville quantum gravity
$\bullet$ Probability on groups (of negative curvature), geometric group theory, ergodic theory, Roe Algebras
$\bullet$ Stochastic homogenization of partial differential equations (e.g. Hamilton-Jacobi-Bellman equations), random walks in random environments and on percolation clusters

Selected Publications

Comets, F; Cosco, C; Mukherjee, C Space-time fluctuation of the Kardar-Parisi-Zhang equation in d≥3 and the Gaussian free field. https://arxiv.org/abs/1905.03200 Vol. 2019, 2019 online
Mukherjee, C; Varadhan, SRS Identification of the Polaron measure in strong coupling and the Pekar variational formula. Annals of Probability Vol. 48 (5), 2020, pp 2119-2144 online
Bröker, Y; Mukherjee, C Localization of the Gaussian multiplicative chaos in the Wiener space and the stochastic heat equation in strong disorder. Annals of Applied Probability Vol. 29 (6), 2019, pp 3745-3785 online
Mukherjee, C; Varadhan, SRS Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times. Communications on Pure and Applied Mathematics Vol. 73 (2), 2020, pp 350-383 online
Mukherjee, C Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equation. Annals of Applied Probability Vol. https://arxiv.org/abs/1706.09345, 2017 online
Berger, N; Mukherjee, C; Okamura, K. Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations. Communications in Mathematical Physics Vol. 358, 2018, pp 633–673 online
Mukherjee, C; Shamov, A; Zeitouni, O Weak and strong disorder for the stochastic heat equation and continuous directed polymers in d≥3. Electronic Communications in Probability Vol. 21, 2016, pp 1-12 online
Bolthausen, E; König, W; Mukherjee, C Mean‐Field Interaction of Brownian Occupation Measures II: A Rigorous Construction of the Pekar Process. Communications on Pure and Applied Mathematics Vol. 70 (8), 2017, pp 1598-1629 online
Mukherjee, C Gibbs Measures on Mutually Interacting Brownian Paths under Singularities. Communications on Pure and Applied Mathematics Vol. 70 (12), 2017, pp 2366-2404 online
Mukherjee, C; Varadhan, SRS Brownian occupation measures, compactness and large deviations. Annals of Probability Vol. 44 (6), 2016, pp 3934-3964 online

Current Publications

Current Publications

$\bullet$ Rodrigo Bazaes, Alexander Mielke, and Chiranjib Mukherjee. Stochastic homogenization for Hamilton-Jacobi-Bellman equations on continuum percolation clusters. arXiv e-prints, August 2022. arXiv:2208.07269.

$\bullet$ Chiranjib Mukherjee. Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equation. Ann. Appl. Probab., 32(3):2028–2062, June 2022. doi:10.1214/21-AAP1727.

$\bullet$ Chiranjib Mukherjee and S. R. S. Varadhan. Corrigendum and addendum: Identification of the Polaron measure I: Fixed coupling regime and the central limit theorem for large times. Comm. Pure Appl. Math., 75(7):1642–1653, April 2022. doi:10.1002/cpa.22052.

$\bullet$ Francis Comets, Clément Cosco, and Chiranjib Mukherjee. Space-time fluctuation of the Kardar-Parisi-Zhang equation in $d \ge 3$ and the Gaussian free field. Ann. Henri Poincaré, January 2022.

$\bullet$ Rodrigo Bazaes, Chiranjib Mukherjee, Alejandro F. Ramírez, and Santiago Saglietti. Quenched and averaged large deviations for random walks in random environments: The impact of disorder. Ann. Appl. Probab., January 2022.

$\bullet$ Rodrigo Bazaes, Chiranjib Mukherjee, Alejandro Ramírez, and Santiago Saglietti. The effect of disorder on quenched and averaged large deviations for random walks in random environments: boundary behavior. arXiv e-prints, January 2021. arXiv:2101.04606v3.

$\bullet$ Chiranjib Mukherjee and Srinivasa R. S. Varadhan. Identification of the polaron measure in strong coupling and the Pekar variational formula. Ann. Probab., 48(5):2119–2144, September 2020. doi:10.1214/19-AOP1392.

$\bullet$ Yannic Bröker and Chiranjib Mukherjee. Geometry of the Gaussian multiplicative chaos in the Wiener space. arXiv e-prints, August 2020. arXiv:2008.04290.

$\bullet$ Chiranjib Mukherjee and S. R. S. Varadhan. The Polaron measure. In Applied Probability and Stochastic Processes, pages 415–419. August 2020. doi:10.1007/978-981-15-5951-8_24.

$\bullet$ Francis Comets, Clément Cosco, and Chiranjib Mukherjee. Renormalizing the Kardar-Parisi-Zhang equation in $d\geq 3$ in weak disorder. J. Stat. Phys., 179(3):713–728, April 2020. doi:10.1007/s10955-020-02539-7.

$\bullet$ Chiranjib Mukherjee and Srinivasa R. S. Varadhan. Identification of the Polaron measure I: Fixed coupling regime and the central limit theorem for large times. Communications on Pure and Applied Mathematics, 73(2):350–383, February 2020. doi:10.1002/cpa.21858.

$\bullet$ Yannic Bröker and Chiranjib Mukherjee. Localization of the Gaussian multiplicative chaos in the Wiener space and the stochastic heat equation in strong disorder. Ann. Appl. Probab., 29(6):3745–3785, December 2019. doi:10.1214/19-AAP1491.

$\bullet$ Stefan Adams and Chiranjib Mukherjee. Commutative diagram of the Gross-Pitaevskii approximation. arXiv e-prints, November 2019. arXiv:1911.09635.

$\bullet$ Gerold Alsmeyer and Chiranjib Mukherjee. On Null-homology and stationary sequences. arXiv e-prints, October 2019. arXiv:1910.07378.

$\bullet$ Rodrigo Bazaes, Chiranjib Mukherjee, Alejandro Ramirez, and Santiago Saglietti. Equality and difference of quenched and averaged large deviation rate functions for random walks in random environments without ballisticity. arXiv e-prints, June 2019. arXiv:1906.05328.

$\bullet$ Yannic Bröker and Chiranjib Mukherjee. Quenched central limit theorem for the stochastic heat equation in weak disorder. In Probability and analysis in interacting physical systems, volume 283 of Springer Proc. Math. Stat., pages 173–189. May 2019. doi:10.1007/978-3-030-15338-0_6.

$\bullet$ Francis Comets, Clement Cosco, and Chiranjib Mukherjee. Space-time fluctuation of the Kardar-Parisi-Zhang equation in $d\geq 3$ and the Gaussian free field. arXiv e-prints, May 2019. arXiv:1905.03200.