相关论文: Hitting properties of a random string

Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, $U$ and $D$. A gambler gains 1 point for each occurrence of $U$ (including overlapping occurrences) and loses 1 point for each…

We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…

We study feature selection in high-dimensional regression under two distinct sources of instability: sampling variability and measurement error in the design matrix. Stability Selection addresses the former through sub-sampling and…

The string propagation in the two-dimensional stringy black-hole is investigated from a new approach. We completely solve the classical and quantum string dynamics in the lorentzian and euclidean regimes. In the lorentzian case all the…

We develop superstring bit models, in which the lightcone transverse coordinates in D spacetime dimensions are replaced with d=D-2 double-valued "flavor" indices $x^k-> f_k=1,2$; $k=2,...,d+1$. In such models the string bits have no space…

We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define…

Making use of the gauge/string duality, it is possible to study some aspects of the string breaking phenomenon in the three quark system. Our results point out that the string breaking distance is not universal and depends on quark…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network…

In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…

In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study…

We investigate stringy excitations in Randall-Sundrum effective theories for electroweak symmetry breaking arising from embedding in string theory. RS is dual to a confining gauge theory, which we expect to have "QCD strings," or color flux…

We introduce so-called chaotic strings (coupled 1-dimensional noise strings underlying the Parisi-Wu approach of stochastic quantization on a small scale) as a possible amendment of ordinary string theories. These strings are strongly…

A string $w$ is said to be a minimal unique substring (MUS) of a string $T$ if $w$ occurs exactly once in $T$, and any proper substring of $w$ occurs at least twice in $T$. It is known that the number of MUSs in a string $T$ of length $n$…

We consider a string theory with two types of strings with geometric interaction. We show that the theory contains strings with constant Dirichlet boundary condition and those strings are glued together by 2-d topological gravity with…

We explain, in a slightly modified form, an old construction allowing to reformulate the U(N) gauge theory defined on a D-dimensional lattice as a theory of lattice strings (a statistical model of random surfaces). The world surface of the…

We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single…

Multiple gauge theories predict the presence of cosmic strings with different mass densities $G\mu/c^2$. We derive an equation governing the perturbations of a rotating black hole pierced by a straight, infinitely long cosmic string along…

We give recurrence and transience criteria for two cases of time-homogeneous Markov chains on the real line with transition kernel $p(x,dy)=f_x(y-x)dy$, where $f_x(y)$ are probability densities of symmetric distributions and, for large…

The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal…