Related papers: Baire categorical aspects of first passage percola…
Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube B_n ={0,1}^n with nearest neighbor edges. For oriented and unoriented percolation, p=e/n and p=1/n are the respective critical…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
First class constraints in a canonical formalism of a gauge theory might generate transformations which map a state to its physically equivalent state. This is called Dirac's conjecture. There are two examples which may be candidates of…
Attempts to find a quantum-to-classical correspondence in a classically forbidden region leads to non-physical paths, involving, for example, complex time or spatial coordinates. Here, we identify genuine quasi-classical paths for tunneling…
In first-passage percolation, we assign i.i.d.~nonnegative weights $(t_e)$ to the nearest-neighbor edges of $\mathbb{Z}^d$ and study the induced pseudometric $T = T(x,y)$. In this paper, we focus on geodesics, or optimal paths for $T$, and…
The aim of this article is to study the forest composed by point-to-line geodesics in the last-passage percolation model with exponential weights. We will show that the location of the root can be described in terms of the maxima of a…
We construct an edge-weight distribution for i.i.d. first-passage percolation on $\mathbb{Z}^2$ whose limit shape is not a polygon and whose extreme points are arbitrarily dense in the boundary. Consequently, the associated Richardson-type…
A natural extension of a right-continuous integer-valued random walk is one which can jump to the right by one or two units. First passage times above a given fixed level then admit a tractable Laplace transform (probability generating…
First passage under restart with branching is proposed as a generalization of first passage under restart. Strong motivation to study this generalization comes from the observation that restart with branching can expedite the completion of…
The metric $D_\alpha (q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $R^d$, defined as the infimum of $(\sum_i |q_i - q_{i+1}|^\alpha)^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending with $q'$…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear flows. The absence of a clear cut instability mechanism, the spatio-temporal intermittent character and extremely long…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time t will have a width of order t^{1/3}. We…
We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as…
The topology of the universe is discussed in relation to the singularity problem. We explore the possibility that the initial state of the universe might have had a structure with 3-Klein bottle topology, which would lead to a model of a…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…