# Multidimensional Random Polymers: A Renewal Approach

@article{Ioffe2014MultidimensionalRP, title={Multidimensional Random Polymers: A Renewal Approach}, author={Dmitry Ioffe}, journal={arXiv: Probability}, year={2014}, pages={147-210} }

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 structures which appear in such models. In the ballistic regime an irreducible decomposition of typical polymers leads to an effective random walk reinterpretation of the latter. In the annealed case the Ornstein-Zernike theory based on this approach paves the way to an essentially complete control on the…

## 13 Citations

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

- Mathematics
- 2018

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…

### Scaling limit of ballistic self-avoiding walk interacting with spatial random permutations

- MathematicsElectronic Journal of Probability
- 2019

We consider nearest neighbour spatial random permutations on Z d . In this case, the energy of the system is proportional to the sum of all cycle lengths, and the system can be interpreted as an…

### Ornstein-Zernike behavior for Ising models with infinite-range interactions

- Mathematics
- 2021

. We prove Ornstein–Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumptions on the…

### Potts Models with a Defect Line

- PhysicsCommunications in Mathematical Physics
- 2018

We provide a detailed analysis of the correlation length in the direction parallel to a line of modified coupling constants in the ferromagnetic Potts model on $${\mathbb{Z}^{d}}$$Zd at temperatures…

### Critical prewetting in the 2d Ising model

- PhysicsThe Annals of Probability
- 2022

In this paper we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a 2N·N…

### Statistics of Projected Motion in One Dimension of a D-Dimensional Random Walker

- Mathematics, Physics
- 2016

We are studying the motion of a random walker in generalised d-dimensional
continuum with unit step length (up to 10 dimensions) and its projected one
dimensional motion numerically. The motion of…

### Biased Random Walk Conditioned on Survival Among Bernoulli Obstacles: Subcritical Phase

- Mathematics
- 2019

We consider a discrete time biased random walk conditioned to avoid Bernoulli obstacles on $${\mathbb {Z}}^d$$ Z d ( $$d\ge 2$$ d ≥ 2 ) up to time N . This model is known to undergo a phase…

### Asymptotics of even–even correlations in the Ising model

- Computer ScienceProbability Theory and Related Fields
- 2018

Finite-range ferromagnetic Ising models on Zd in the regime ofbeta < β c are considered, which shows the behavior of the prefactor to the exponential decay of Cov(σA,σB), for arbitrary finite sets A and B of even cardinality, as the distance between A and A diverges.

### Invariance Principle for a Potts Interface Along a Wall

- MathematicsJournal of Statistical Physics
- 2020

We consider nearest-neighbour two-dimensional Potts models, with boundary conditions leading to the presence of an interface along the bottom wall of the box. We show that, after a suitable diffusive…

### Invariance Principle for a Potts Interface Along a Wall

- MathematicsJournal of Statistical Physics
- 2020

We consider nearest-neighbour two-dimensional Potts models, with boundary conditions leading to the presence of an interface along the bottom wall of the box. We show that, after a suitable diffusive…

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