## Wioletta Ruszel

34 records found

1

## Authored

## Scaling Limits in Divisible Sandpiles

### A Fourier Multiplier Approach

In this paper we investigate scaling limits of the odometer in divisible sandpiles on d-dimensional tori following up the works of Chiarini et al. (Odometer of long-range sandpiles in the torus: mean behaviour and scaling limits, 2018), Cipriani et al. (Probab Theory Relat Fie ...

In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration - 1 is the only metastable state and we estimate the mean exit time. Moreover, we illustrate the theory wi ...

We show that in Abelian sandpiles on infinite Galton–Watson trees, the probability that the total avalanche has more than t topplings decays as t^{- 1 / 2}. We prove both quenched and annealed bounds, under suitable moment conditions. Our proofs are based on an analysi
...

## Contour Methods for Long-Range Ising Models

### Weakening Nearest-Neighbor Interactions and Adding Decaying Fields

We consider ferromagnetic long-range Ising models which display phase transitions. They are one-dimensional Ising ferromagnets, in which the interaction is given by Jx,y=J(|x-y|)≡1|x-y|2-α with α∈ [0 , 1) , in particular, J(1) = 1. For this class of models, one way in which on ...

## Contour Methods for Long-Range Ising Models

### Weakening Nearest-Neighbor Interactions and Adding Decaying Fields

We consider ferromagnetic long-range Ising models which display phase transitions. They are one-dimensional Ising ferromagnets, in which the interaction is given by Jx,y=J(|x-y|)≡1|x-y|2-α with α∈ [0 , 1) , in particular, J(1) = 1. For this class of models, one way in which on ...

We consider the two-dimensional Ising model with long-range pair interactions of the form (Formula presented.) with (Formula presented.), mostly when (Formula presented.). We show that Dobrushin states (i.e. extremal non-translation-invariant Gibbs states selected by mixed ± b ...

## Contributed

## Quantum Error Correction

### Decoders for the Toric Code

## Critical behavior of Ising spin systems

### Phase transition, metastability and ergodicity

In this thesis we shall consider a generalization on Pólya Processes as have been described by Chung et al. [7]. Given finitely many bins, containing an initial configuration of balls, additional balls arrive one at a time. For each new ball, a new bin is cre ...

^{p}(T) boundary function. First, we will focus on the holomorphic version of the Dirichlet problem and introduce Hardy space theory, from which will follow a sufficient condition on the Fourier coeffi ...