Related papers: Computing Large Deviations of First-Passage-Time S…
Even after decades of research the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time $\tau$, we…
We prove non-universality results for first-passage percolation on the configuration model with i.i.d. degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of…
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual…
Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from…
The generalized Jeffreys-type law is formulated as a multi-term time-fractional Jeffreys-type equation, whose dynamics exhibit rich scaling crossover phenomena entailing different diffusion mechanisms. In this work, we provide a novel…
The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble of LP problems with $n$ variables and…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
The ``first passage-time'' (FPT) problem is an important problem with a wide range of applications in mathematics, physics, biology and finance. Mathematically, such a problem can be reduced to estimating the probability of a (stochastic)…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
We develop a scheme for the computation of the full-counting statistics of transport described by Markovian master equations with an arbitrary time dependence. It is based on a hierarchy of generalized density operators, where the trace of…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
In biological, glassy, and active systems, various tracers exhibit Laplace-like, i.e., exponential, spreading of the diffusing packet of particles. The limitations of the central limit theorem in fully capturing the behaviors of such…
Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…
We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…
Many problems in finance require the information on the first passage time (FPT) of a stochastic process. Mathematically, such problems are often reduced to the evaluation of the probability density of the time for such a process to cross a…
We are interested in analyzing the effect of bandwidth sharing for telecommunication networks. More precisely, we want to calculate which routes are bottlenecks by means of large deviations techniques. The method is illustrated in this…
The problem of identifiability of model parameters for open quantum systems is considered by investigating two-level dephasing systems. We discuss under which conditions full information about the Hamiltonian and dephasing parameters can be…