Related Experiment Video
Updated: Mar 15, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Probability distributions for directed polymers in random media with correlated noise
1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Abstract:
The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in d=1+1 dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified in the presence of spatially correlated noise. The width of the distribution scales as the DPRM length to an exponent β, in good (but not full) agreement with previous renormalization group and numerical results. The scaled probability is well described by the Tracy-Widom form for uncorrelated noise, but becomes symmetric with increasing correlation exponent. We thus find a class of distributions that continuously interpolates between Tracy-Widom and Gaussian forms.
More Related Videos
Related Concept Videos
Polymers: Molecular Weight Distribution
Molecular Weight of Step-Growth Polymers
As the step-growth polymerization involves step-wise condensation of monomers, the molecular weight also builds up eventually. Consequently, high molecular weight polymers are obtained at the late stages of the polymerization, where 99% of monomers have been consumed.
The extent of the...
Probability Distributions
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
Polymers: Defining Molecular Weight
The number average molecular weight (Mn) is the summation of the number...
Ziegler–Natta Chain-Growth Polymerization: Overview
Poisson Probability Distribution
The...

