Related papers: Heavy Hitters and Bernoulli Convolutions
We propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
Hierarchical time series are common in several applied fields. The forecasts for these time series are required to be coherent, that is, to satisfy the constraints given by the hierarchy. The most popular technique to enforce coherence is…
We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and…
In this paper we consider an irreducible random walk on the integer lattice $\mathbb{Z}$ that is in the domain of normal attraction of a strictly stable process with index $\alpha\in (1, 2)$ and obtain the asymptotic form of the…
In particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling…
In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…
In this note, an alternative for presenting the distribution of `significant' events in searches for new phenomena is described. The alternative is based on probability density functions used in the evaluation of the `significance' of an…
A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being $+1$ or -1, equally likely. The other families cited in the title are Bernoulli random walks under various conditionings. A peak…
We present a novel application of the HHL (Harrow-Hassidim-Lloyd) algorithm -- a quantum algorithm solving systems of linear equations -- in solving an open problem about quantum random walks, namely computing hitting (or absorption)…
In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential…
Threshold selection plays a key role for various aspects of statistical inference of rare events. Most classical approaches tackling this problem for heavy-tailed distributions crucially depend on tuning parameters or critical values to be…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
Extreme events have low occurrence probabilities and display pronounced deviation from their average behaviour, such as earthquakes or power blackouts. Such extreme events occurring on the nodes of a complex network have been extensively…
A result of Chebyshev (1864) and Hoeffding1956}, on bounding an expectation of a given function with respect to a Bernoulli convolution (also called Poisson binomial law, or law of the number of successes in independent trials) with any…
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…