Related papers: Notes on oriented percolation
Corrections to a mean number of droplets appeared in the process of nucleation have been analyzed. The two stage model with a fixed boundary can not lead to a write result. The multi stage generalization of this model also can not give…
Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
Conventional machine learning studies generally assume close-environment scenarios where important factors of the learning process hold invariant. With the great success of machine learning, nowadays, more and more practical tasks,…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
This paper has been withdraw by the authors. An enlarged and complete analysis of the constraints is presented in hep-th/9910163. It includes also relativistic particles and strings. The non-relativistic particle quantization has been…
The present work proposes the concept of induced percolation over multiple-object systems, so that features such as the number of merged clusters can be used as a relevant measurement. The suggested approach involves the expansion of the…
In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
We investigate how knowledge percolates and clusters in a given knowledge space. We introduce a simple model of knowledge organization in which each contribution spans a certain number of items. If this contribution overlaps with others…
In the last few years, the theory of decentralized distributed convex optimization has made significant progress. The lower bounds on communications rounds and oracle calls have appeared, as well as methods that reach both of these bounds.…
We study the galaxy alignment in the sample of very rich Abell clusters located in and outside superclusters. The statistically significant difference among investigated samples exists. We found that in contrast to whole sample of cluster,…
We have generalized the idea of backbend in a nearest-neighbor oriented bond percolation process by considering a backbend sequence $\beta : \mathbb{Z}_+ \to \mathbb{Z}_+ \cup \{\infty\}$, and defining a $\beta$-backbend path from the…
This paper has been withdrawn because the models on which it was based have undergone significant changes and improvements. A new paper with the same title, based on the improved models, is accepted for publication in MNRAS and is available…
We study oriented percolation on random causal triangulations, those are random planar graphs obtained roughly speaking by adding horizontal connections between vertices of an infinite tree. When the underlying tree is a geometric…
We study two new models of two particle species invading a surface from opposite sides. Collisions of particles of different species lead to the formation of congestion fronts. One of the models implements a reversible process whereas in…
In this paper we review the recent advances on explosive percolation, a very sharp phase transition first observed by Achlioptas et al. (Science, 2009). There a simple model was proposed, which changed slightly the classical percolation…
We analyze the percolation properties of certain clusters defined on configurations of the 2--dimensional Heisenberg model. We find that, given any direction \vec{n} in O(3) space, the spins almost perpendicular to \vec{n} form a…
This draft is intended to be used as class notes for a grad course on rigorous statistical mechanics at math department of UFMG. It should be considered as a very prelimivary version and a work in progress. Several chapters lack references,…