# Annealed scaling for a charged polymer in dimensions two and higher

@article{Berger2017AnnealedSF, title={Annealed scaling for a charged polymer in dimensions two and higher}, author={Quentin Berger and Frank den Hollander and Julien Poisat}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2017}, volume={51} }

This paper considers an undirected polymer chain on Zd, d⩾2, with i.i.d. random charges attached to its constituent monomers. Each self-intersection of the polymer chain contributes an energy to the interaction Hamiltonian that is equal to the product of the charges of the two monomers that meet. The joint probability distribution for the polymer chain and the charges is given by the Gibbs distribution associated with the interaction Hamiltonian. The object of interest is the annealed free…

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## References

SHOWING 1-10 OF 23 REFERENCES

### Annealed Scaling for a Charged Polymer

- Mathematics
- 2015

This paper studies an undirected polymer chain living on the one-dimensional integer lattice and carrying i.i.d. random charges. Each self-intersection of the polymer chain contributes to the…

### Multidimensional Random Polymers: A Renewal Approach

- Materials Science
- 2015

In these lecture notes we discuss ballistic phase of quenched and annealed stretched polymers in random environment on \(\mathbb{Z}^{d}\) with an emphasis on the natural renormalized renewal…

### Random Walk Intersections: Large Deviations and Related Topics

- Mathematics
- 2010

The material covered in this book involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and…

### Long-time tails in the parabolic Anderson model

- Mathematics
- 2000

We consider the parabolic Anderson problem ∂ t u = κΔu + ξu on (0, ∞) × Z d with random i.i.d. potential ξ = (ξ(z)) z ∈ Zd and the initial condition u(0,.) ≡ 1. Our main assumption is that esssup…

### JOINT DENSITY FOR THE LOCAL TIMES OF CONTINUOUS-TIME MARKOV CHAINS: EXTENDED VERSION

- Mathematics
- 2005

We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density…

### A large-deviation result for the range of random walk and for the Wiener sausage

- Mathematics
- 2001

Abstract. Let {Sn} be a random walk on ℤd and let Rn be the number of different points among 0, S1,…, Sn−1. We prove here that if d≥ 2, then ψ(x) := limn→∞(−:1/n) logP{Rn≥nx} exists for x≥ 0 and…

### An invariance principle for random walk bridges conditioned to stay positive

- Mathematics
- 2012

We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the…

### On the Equivalence of Euler-Lagrange and Noether Equations

- Mathematics
- 2013

We prove that, under the condition of nontriviality, the Euler-Lagrange and Noether equations are equivalent for a general class of scalar variational problems. Examples are position independent…

### An Introduction To Probability Theory And Its Applications

- Mathematics
- 1950

A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.

### Large Deviations (Fields Institute Monographs vol 14) (Providence RI: American Mathematical Society

- 2000