Private Homepagehttps://www.uni-muenster.de/Stochastik/en/Arbeitsgruppen/Mukherjee/
Research InterestsLarge deviations and stochastic analysis
Directed polymers, stochastic PDEs, multiplicative chaos
Stochastic homogenization, Hamilton-Jacobi equations
Percolation, geometric group theory, C* algebras
Selected PublicationsMukherjee, C; Varadhan, SRS Brownian occupation measures, compactness and large deviations. Annals of Probability Vol. 44 (6), 2016, pp 3934-3964 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; 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
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
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
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; 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; 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
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
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
Project membership
Mathematics Münster


C: Models and Approximations

C2: Multi-scale phenomena and macroscopic structures
C3: Interacting particle systems and phase transitions
Current PublicationsBazaes Rodrigo, Mukherjee Chiranjib, Ramírez Alejandro, Saglietti Santiago The effect of disorder on quenched and averaged large deviations for random walks in random environments: boundary behavior. https://arxiv.org/abs/2101.04606 Vol. na, 2021 online
Comets, F; Cosco, C; Mukherjee, C Renormalizing the Kardar-Parisi-Zhang equation in d≥3 in weak disorder. Journal of Statistical Physics Vol. 179, 2020, pp 713-728 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
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
Bröker, Yannic and Mukherjee, Chiranjib Geometry of the Gaussian multiplicative chaos in the Wiener space. https://arxiv.org/abs/2008.04290 Vol. na, 2020 online
Bröker, Y; Comets, F; Cosco; C; Mukherjee, C; Shamov, A; Zeitouni; O KPZ equation in d ≥ 3 and construction of Gaussian multiplicative chaos in the Wiener space. , 2019 online
Adams, S; Mukherjee, C Commutative diagram of the Gross-Pitaevskii approximation. https://arxiv.org/abs/1911.09635 Vol. 2019, 2019 online
Altmeyer, G; Mukherjee, C On Null-homology and stationary sequences. https://arxiv.org/abs/1910.07378 Vol. 2019, 2019 online
Bazaes, R; Mukherjee, C; Ramirez, A; Saglietti, S Quenched and averaged large deviation rate functions for random walks in random environments: the impact of disorder. https://arxiv.org/abs/1906.05328 Vol. 2019, 2019 online
Current ProjectsEXC 2044 - C2: Multi-scale phenomena and macroscopic structures In multi-scale problems, geometry and dynamics on the micro-scale influence structures on coarser scales. In this research unit we will investigate and analyse such structural interdependence based on topological, geometrical or dynamical properties of the underlying processes.

We are interested in transport-dominated processes, such as in the problem of how efficient a fluid can be stirred to enhance mixing, and in the related analytical questions. A major concern will be the role of molecular diffusion and its interplay with the stirring process. High Péclet number flow in porous media with reaction at the surface of the porous material will be studied. Here, the flowinduces pore-scale fluctuations that lead to macroscopic enhanced diffusion and reaction kinetics. We also aim at understanding advection-dominated homogenisation problems in random regimes.

We aim at classifying micro-scale geometry or topology with respect to the macroscopic behaviour of processes considered therein. Examples are meta material modelling and the analysis of processes in biological material. Motivated by network formation and fracture mechanics in random media, we will analyse the effective behaviour of curve and free-discontinuity energies with stochastic inhomogeneity. Furthermore, we are interested in adaptive algorithms that can balance the various design parameters arising in multi-scale methods. The analysis of such algorithms will be the key towards an optimal distribution of computational resources for multi-scale problems.

Finally, we will study multi-scale energy landscapes and analyse asymptotic behaviour of hierarchical patterns occurring in variational models for transportation networks and related optimal transport problems. In particular, we will treat questions of self-similarity, cost distribution, and locality of the fine-scale pattern. We will establish new multilevel stochastic approximation algorithms with the aim of numerical optimisation in high dimensions. online
EXC 2044 - C3: Interacting particle systems and phase transitions The question of whether a system undergoes phase transitions and what the critical parameters are is intrinsically related to the structure and geometry of the underlying space. We will study such phase transitions for variational models, for processes in random environments, for interacting particle systems, and for complex networks. Of special interest are the combined effects of fine-scalerandomly distributed heterogeneities and small gradient perturbations.

We aim to connect different existing variational formulations for transportation networks, image segmentation, and fracture mechanics and explore the resulting implications on modelling, analysis, and numerical simulation of such processes. We will study various aspects of complex networks, i.e. sequences of random graphs (Gn)n∈N, asking for limit theorems as n tends to infinity. A main task will be to broaden the class of networks that can be investigated, in particular, models which include geometry and evolve in time. We will study Ising models on random networks or with random interactions, i.e. spin glasses. Fluctuations of order parameters and free energies will be analysed, especially at the critical values where the system undergoes a phase transition. We will also investigate whether a new class of interacting quantum fields connected with random matrices and non-commutative geometry satisfies the Osterwalder-Schrader axioms. Further, we will study condensation phenomena, where complex network models combine the preferential attachment paradigm with the concept of fitness. In the condensation regime, a certain fraction of the total mass dynamically accumulates at one point, the condensate. The aim is a qualitative and quantitative analysis of the condensation. We willalso explore connections to structured population models. Further, we will study interacting particle systems on graphs that describe social interaction or information exchange. Examples are the averaging process or the Deffuant model.

We will also analyse asymmetric exclusion processes (ASEP) on arbitrary network structures. An interesting aspect will be how these processes are influenced by different distribution mechanisms of the particles at networks nodes. If the graph is given by a lattice, we aim to derive hydrodynamic limits for the ASEP with jumps of different ranges for multiple species, and for stochastic interactingmany-particle models of reinforced random walks. Formally, local cross-diffusion syste ms are obtained as limits of the classical multi-species ASEP and of the many-particle random walk. We will compare the newly resulting limiting equations and are interested in fluctuations, pattern formation, and the long-time behaviour of these models on the microscopic and the macroscopic scale. Further, we will analyse properties of the continuous directed polymer in a random environment. online
E-Mailchiranjib dot mukherjee at uni-muenster dot de
Phone+49 251 83-33772
FAX+49 251 83-32712
Room130.012
Secretary   Sekretariat Kollwitz
Frau Anita Kollwitz
Telefon +49 251 83-33770
Fax +49 251 83-32712
Zimmer 130.030
AddressProf. Dr. Chiranjib Mukherjee
Institut für Mathematische Stochastik
Fachbereich Mathematik und Informatik der Universität Münster
Orléans-Ring 10
48149 Münster
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