27 citations · 110 across the 23 of their papers we have counts for
24 papers · 1 filter
Positive and negative moments for directed polymers in random environment in weak disorder
Rodrigo Bazaes, Chiranjib Mukherjee
Very recently, Junk [11] showed that for directed polymers in bounded random environments, the weak disorder (uniform integrable) phase implies that the polymer martingale is bound…
Subcritical Gaussian Multiplicative Chaos in the Wiener Space: Construction, Moments and Volume Decay
Rodrigo Bazaes, Isabel Lammers, Chiranjib Mukherjee
We construct and study properties of an infinite dimensional analog of Kahane's theory of Gaussian multiplicative chaos \cite{K85}. Namely, if is a random field defined w.…
The effect of disorder on quenched and averaged large deviations for random walks in random environments: boundary behavior
Rodrigo Bazaes, Chiranjib Mukherjee, Alejandro Ramírez +1
For a random walk in a uniformly elliptic and i.i.d. environment on with , we show that the quenched and annealed large deviations rate functions agree on a…
Geometry of the Gaussian multiplicative chaos in the Wiener space
Yannic Bröker, Chiranjib Mukherjee
We develop an approach for investigating geometric properties of Gaussian multiplicative chaos (GMC) in an infinite dimensional set up. The base space is chosen to be the space of…
Commutative diagram of the Gross-Pitaevskii approximation
Stefan Adams, Chiranjib Mukherjee, Quirin Vogel
It is well-known that the Gross-Pitaevskii variational formula describes the ground-state energy per particle of -indistinguishable trapped particles (Bosons) in a dilute state…
On Null-homology and stationary sequences
Gerold Alsmeyer, Chiranjib Mukherjee
The concept of homology, originally developed as a useful tool in algebraic topology, has by now become pervasive in quite different branches of mathematics. The notion particularl…
Quenched and averaged large deviation rate functions for random walks in random environments: the impact of disorder
Rodrigo Bazaes, Chiranjib Mukherjee, Alejandro Ramirez +1
In 2003, Varadhan [V03] developed a robust method for proving quenched and averaged large deviations for random walks in a uniformly elliptic and i.i.d. environment (RWRE) on $\mat…
Space-time fluctuation of the Kardar-Parisi-Zhang equation in and the Gaussian free field
Francis Comets, Clément Cosco, Chiranjib Mukherjee
We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for : $$ \frac{\partial}{\partial t} h_{\varepsilon} = \frac12 Δh_{\varepsilon} + \bigg[\f…
Renormalizing the Kardar-Parisi-Zhang equation in in weak disorder
Francis Comets, Clement Cosco, Chiranjib Mukherjee
We study Kardar-Parisi-Zhang equation in spatial dimension 3 or larger driven by a Gaussian space-time white noise with a small convolution in space. When the noise intensity is sm…
Identification of the Polaron measure in strong coupling and the Pekar variational formula
Chiranjib Mukherjee, S. R. S. Varadhan
The path measure corresponding to the Fröhlich Polaron appearing in quantum statistical mechanics is defined as the tilted measure $$ \widehat{\mathbb P}_{\varepsilon,T}= \frac{1}{…
Localization of the Gaussian multiplicative chaos in the Wiener space and the stochastic heat equation in strong disorder
Yannic Bröker, Chiranjib Mukherjee
We consider a {\it{Gaussian multiplicative chaos}} (GMC) measure on the classical Wiener space driven by a smoothened (Gaussian) space-time white noise. For it was shown…
Fluctuation and Rate of Convergence for the Stochastic Heat Equation in Weak Disorder
Francis Comets, Clément Cosco, Chiranjib Mukherjee
We consider the stochastic heat equation on with multiplicative space-time white noise noise smoothed in space. For and small noise intensity, the solution…
Strong coupling limit of the Polaron measure and the Pekar process
Chiranjib Mukherjee, S. R. S. Varadhan
The {\it{Polaron measure}} is defined as the transformed path measure $$\widehat{\mathbb P}_{ε,T}= Z_{ε,T}^{-1}\,\, \exp\bigg\{\frac{1}{2}\int_{-T}^T\int_{-T}^T\frac{ε\e^{-ε|t-s|}}…
Identification of the Polaron measure I: Fixed coupling regime and the central limit theorem for large times
Chiranjib Mukherjee, S. R. S. Varadhan
We consider the Fröhlich model of the Polaron whose path integral formulation leads to the transformed path measure $$ \widehat{\mathbb P}_{α,T}(\mathrm dω)= Z_{α,T}^{-1}\,\, \exp\…
Quenched central limit theorem for the stochastic heat equation in weak disorder
Yannic Broeker, Chiranjib Mukherjee
We continue with the study of the mollified stochastic heat equation in given by with spatially smoothene…
Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equation
Chiranjib Mukherjee
We consider a class of Gibbs measures defined with respect to increments of -dimensional Wiener measure, with the underlying Hamiltonian carrying interacti…
Quenched large deviations for simple random walks on percolation models including long-range correlations
Noam Berger, Chiranjib Mukherjee, Kazuki Okamura
We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on (). The models under in…
Weak and Strong disorder for the stochastic heat equation and the continuous directed polymer in
Chiranjib Mukherjee, Alexander Shamov, Ofer Zeitouni
We consider the smoothed multiplicative noise stochastic heat equation $$d u_{\eps,t}= \frac 12 Δu_{\eps,t} d t+ β\eps^{\frac{d-2}{2}}\, \, u_{\eps, t} \, d B_{\eps,t} , \;\;u_{\ep…
Mean-Field interacton of Brownian occupation measures. II: A rigorous construction of the Pekar process
Erwin Bolthausen, Wolfgang Koenig, Chiranjib Mukherjee
We consider mean-field interactions corresponding to Gibbs measures on interacting Brownian paths in three dimensions. The interaction is self-attractive and is given by a singular…
Gibbs measures on mutually interacting Brownian paths under singularities
Chiranjib Mukherjee
We are interested in the analysis of Gibbs measures defined on two independent Brownian paths in interacting through a mutual self-attraction. This is expressed by th…
Mean-field interaction of Brownian occupation measures, I: uniform tube property of the Coulomb functional
Wolfgang Koenig, Chiranjib Mukherjee
We study the transformed path measure arising from the self-interaction of a three-dimensional Brownian motion via an exponential tilt with the Coulomb energy of the occupation mea…
Quenched Large Deviations for Simple Random Walks on Supercritical Percolation Clusters
Noam Berger, Chiranjib Mukherjee
We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster on , .. We take the point of view of the m…
Brownian Occupation Measures, Compactness and Large Deviations
Chiranjib Mukherjee, S. R. S. Varadhan
In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed…
Large Deviations for Brownian Intersection Measures
Wolfgang Koenig, Chiranjib Mukherjee
We consider independent Brownian motions in . We assume that and . Let denote the intersection measure of the paths by time , i.e., th…