**Prof. Dr. Chiranjib MukherjeeInstitut für Mathematische StochastikInvestigator in Mathematics MünsterEmail Address: chiranjib dot mukherjee at uni-muenster dot dePersonal web page: Prof. Dr. Chiranjib Mukherjee**

**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

• **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**

$\bullet $ **Rodrigo Bazaes** and **Chiranjib Mukherjee**.
Positive and negative moments for directed polymers in random environment in weak disorder.
*arXiv e-prints*, December 2022.
arXiv:2212.06029.

$\bullet $ **Chiranjib Mukherjee** and **Konstantin Recke**.
Schur multipliers of $C^*$-algebras, group-invariant compactification and applications to amenability and percolation.
*arXiv e-prints*, November 2022.
arXiv:2211.11411.

$\bullet $ **Rodrigo Bazaes**, **Isabel Lammers**, and **Chiranjib Mukherjee**.
Subcritical Gaussian multiplicative chaos in the Wiener space: Construction, moments and volume decay.
*arXiv e-prints*, November 2022.
arXiv:2211.08996.

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

$\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.