Related papers: Symmetry classes of classical stochastic processes
We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of…
We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a new process whose…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
We introduce an algorithm for generating a random sequence of fragmentation trees, which we call the ancestral branching algorithm. This algorithm builds on the recursive partitioning structure of a tree and gives rise to an associated…
We study Markovian symmetry and non-symmetry random evolutions in $\mathbf{R}^n$. Weak convergence of Markovian symmetry random evolution to Wiener process and of Markovian non-symmetry random evolution to a diffusion process with drift is…
The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…
We study a class of quantum Markov processes that, on the one hand, is inspired by the micromaser experiment in quantum optics and, on the other hand, by classical birth and death processes. We prove some general geometric properties and…
We define symmetric and asymmetric branching trees, a class of processes particularly suited for modeling genealogies of inhomogeneous populations where individuals may reproduce throughout life. In this framework, a broad class of…
This paper provides full classification of dynamics for continuous time Markov chains (CTMCs) on the non-negative integers with polynomial transition rate functions. Such stochastic processes are abundant in applications, in particular in…
Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
We classify the Markov chains that can be generated on the set of quantum states by a unitarily evolving 3-dim quantum system (qutrit) that is repeatedly measured with a projective measurement (PVM) consisting of one rank-2 projection and…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
The parallel strong-scaling of Krylov iterative methods is largely determined by the number of global reductions required at each iteration. The GMRES and Krylov-Schur algorithms employ the Arnoldi algorithm for nonsymmetric matrices. The…
We obtain a new relation between the distributions $\mu_t$ at different times $t\ge 0$ of the continuous-time TASEP (Totally Asymmetric Simple Exclusion Process) started from the step initial configuration. Namely, we present a…
Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found…