Related papers: Directed Paths in Random Media
The wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each…
Radio propagation modeling is essential in telecommunication research, as radio channels result from complex interactions with environmental objects. Recently, Machine Learning has been attracting attention as a potential alternative to…
This paper studies the problem of predicting the distribution over multiple possible future paths of people as they move through various visual scenes. We make two main contributions. The first contribution is a new dataset, created in a…
Rendering volumetric scattering media, including clouds, fog, smoke, and other complex materials, is crucial for realism in computer graphics. Traditional path tracing, while unbiased, requires many long path samples to converge in scenes…
This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Predicting human behavior is a difficult and crucial task required for motion planning. It is challenging in large part due to the highly uncertain and multi-modal set of possible outcomes in real-world domains such as autonomous driving.…
Respondent-driven sampling (RDS) is a sampling scheme used in socially connected human populations lacking a sampling frame. One of the first steps to make design-based inferences from RDS data is to estimate the sampling probabilities. A…
We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the…
Here, extending our previous work on this topic, we derive a dynamic closed-form dispersion relation for a rigorous analysis of guided wave propagation along coupled parallel linear arrays of plasmonic nanoparticles, operating as optical…
We present a new solution of the asymmetric two-matrix model in the large $N$ limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with…
This letter presents a unified analytical framework for internodal distance distributions in 2D and 3D wireless networks, with nodes confined to concentric circular or spherical regions. Four deployment scenarios are considered, covering…
Spatial branching processes became increasingly popular in the past decades, not only because of their obvious connection to biology, but also because superprocesses are intimately related to nonlinear partial differential equations.…
Random lasers (RL) emit light through multiple scattering in disordered gain media, typically resulting in isotropic emission with limited directionality control. Controlling RL emission direction in compact systems remains a challenge.…
We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…
Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…