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A model for the solar coronal magnetic field is proposed where multiple directed loops evolve in space and time. Loops injected at small scales are anchored by footpoints of opposite polarity moving randomly on a surface. Nearby footpoints…
We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$.…
This article begins with the discussions on the formation of speckles in the case of non-coherent quasi monochromatic source and of ways to detect them. Prior to this, a brief introduction on the behavior of the atmosphere and its effect on…
We consider upper level-sets of the Gaussian free field on $\mathbb Z^d$, for $d\geq 3$, above a given real-valued height parameter $h$. As $h$ varies, this defines a canonical percolation model with strong, algebraically decaying…
Large surveys of the local Universe have shown that galaxies with different intrinsic properties, such as colour, luminosity and morphological type display a range of clustering amplitudes. Galaxies are therefore not faithful tracers of the…
We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…
We give several algebraic bounds for percolation on directed and undirected graphs: proliferation of strongly-connected clusters, proliferation of in- and out-clusters, and the transition associated with the number of giant components.
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
A basic assumption in current halo occupation model is that the properties of a galaxy depend only on the mass of its dark matter halo. An important consequence of this is that the segregation of the galaxy population by large-scale…
Ptychography involves a sample being illuminated by a coherent, localised probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the probe or sample is shifted…
In these Lectures, I review various extensions of the Lambda-Cold Dark Matter model, characterized by additional light degrees of freedom in the dark sector. In order to reproduce the successful phenomenology of GR in the solar system,…
We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K $\subset$ R d with non empty interior. In a first setting, the Boolean model is a…
We consider a geometric percolation process partially motivated by recent work of Hejda and Kala. Specifically, we start with an initial set $X \subseteq \mathbb{Z}^2$, and then iteratively check whether there exists a triangle $T \subseteq…
We theoretically show that the frequency and momentum of a photon are not necessarily proportional to one another at low frequencies in photonic crystals comprising materials with positive- and negative-valued material properties. We…
We present a completely perturbative model that displays behavior similar to that of walking technicolor. In one phase of the model RG-trajectories run towards an IR-fixed point but approximate scale invariance is spontaneously broken…
Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…
We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x'$, and subsequently take the limit as $|x|$, $|x'|$ as well as $|x-x'|$ diverge to infinity.…
We introduce and study a model of percolation with constant freezing (PCF) where edges open at constant rate 1, and clusters freeze at rate \alpha independently of their size. Our main result is that the infinite volume process can be…
We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses $k \ge 1$ incident edges, whose weight is then increased by 1. The choice of this $k$-tuple occurs…
The purpose of this work is to provide theoretically grounded assessment on both the field-of-view and the bandwidth of a lensless holographic setup. Indeed, while previous works have presented results with super-resolution and…