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We study the fluctuations in equilibrium of a class of Brownian motions interacting through a potential. For a certain choice of exponential potential, the distribution of the system coincides with differences of free energies of the stationary semi-discrete or OConnell-Yor polymer. We show that for Gaussian potentials, the fluctuations are of order $N^{frac{1}{4}}$ when the time and system size coincide, whereas for a class of more general convex potentials $V$ the fluctuations are of order at most $N^{frac{1}{3}}$. In the OConnell-Yor case, we recover the known upper bounds for the fluctuation exponents using a dynamical approach, without reference to the polymer partition function interpretation.
We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magn
We compute the fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate regime. This regime corresponds to taking the inverse temperature to zero with the size of the system. The expone
We derive rigorous bounds on the average momentum occupation numbers $langle n_{mathbf{k}sigma}rangle$ in the Hubbard and Kondo models in the ground state and at non-zero temperature ($T>0$) in the grand canonical ensemble. For the Hubbard model with
We provide a complete proof of the diagrammatic bounds on the lace-expansion coefficients for oriented percolation, which are used in [arXiv:math/0703455] to investigate critical behavior for long-range oriented percolation above 2min{alpha,2} spatial dimensions.
We consider symmetric activated random walks on $mathbb{Z}$, and show that the critical density $zeta_c$ satisfies $csqrt{lambda} leq zeta_c(lambda) leq C sqrt{lambda}$ where $lambda$ denotes the sleep rate.