Related papers: Percolation since Saint-Flour
It is well known that a continuous phase transition in Bernoulli bond percolation on the integer lattice is equivalent to a vanishing probability a vertex is invaded in invasion percolation. We provide a coupling between invasion…
We survey some results and applications of last percolation models of which the limiting distribution can be evaluated.
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…
The first papers on neutrino oscillations are shortly reviewed.
For directed last passage percolation on $\mathbb{Z}^2$ with exponential passage times on the vertices, let $T_{n}$ denote the last passage time from $(0,0)$ to $(n,n)$. We consider asymptotic two point correlation functions of the sequence…
I comment on a recent preprint "A Proposal to Measure Photon-Photon Scattering" that appeared recently as arXiv:1106.0465v1 [hep-ph].
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
These are the notes corresponding to the course given at the IAS-Park City graduate summer school in July 2007.
This paper discusses first passage percolation and flooding on large weighted sparse random graphs with two types of nodes: active and passive nodes. In mathematical physics passive nodes can be interpreted as closed gates where fluid flow…
The introduction to this review summarizes chromosphere observation in two figures. The first part showcases the historical emphasis on the eclipse chromosphere in the development of NLTE line formation theory and criticizes 1D modeling.…
A comment on ``Metallization of Fluid Nitrogen and the Mott Transition in Highly Compressed Low-Z Fluids'' by Chau et al, Phys. Rev. Lett. 90, 245501 (2003).
The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.
We consider first-passage percolation on the edges of $\mathbb{Z}^2 \times \{1, \cdots, k\},$ namely the slab $\mathbb{S}_k$ of width $k$. Each edge is assigned independently a passage time of either 0 (with probability $p_c(\mathbb{S}_k)$)…
We present short proofs of the transcendence of the Liouville and the Mahler numbers. The first proof is known for a long time, the second proof apparently appeared only in 2002-2003. The proofs are accessible to high-school students.
These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.
In 2015, Francis Comets shared with me a clever way to relate a model of directed last passage percolation with i.i.d. Gumbel edge weights to a special case of the log-gamma directed polymer model. To my knowledge, he never wrote this down.…
In the first part I set out some unexplored historical material about the early development of cosmic topology. In the second part I briefly comment new developments in the field since the Lachieze-Rey & Luminet report (1995), both from a…
The precise nature of photospheric flows, and of the transport effects they give rise to, has been the subject of intense debate in the last decade. Here we attempt to give a brief review of the subject emphasizing interdisciplinary (solar…
These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining what is a first-passage process and presenting the…
We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using…