Related papers: On stopping Fock-space processes
We introduce a simple zero-range process with constant rates and one fast rate for a particular occupation number, which diverges with the system size. Surprisingly, this minor modification induces a condensation transition in the…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
This paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process unfolding in an old-fashioned configuration space according to ordinary notions of probability. This argument is based on an…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with stationary increments \xi should be sampled, for the sampled process \xi(\lfloor\cdot…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
In this essay, I develop order-theoretic notions of determinism and contextuality on domains and topoi. In the process, I develop a method for quantifying contextuality and show that the order-theoretic sense of contextuality is analogous…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
Contextuality is a fundamental property of quantum theory and a critical resource for quantum computation. Here, we experimentally observe the arguably cleanest form of contextuality in quantum theory [A. Cabello \emph{et al.}, Phys. Rev.…
Stochastic hydrodynamics is a central tool in the study of first order phase transitions at a fundamental level. Combined with sophisticated free energy models, e.g. as developed in classical Density Functional Theory, complex processes…
This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…
In a noncontextual hidden variable model of quantum theory, hidden variables determine the outcomes of every measurement in a manner that is independent of how the measurement is implemented. Using a generalization of this notion to…
We show how continuous matrix product states of quantum field theories can be described in terms of the dissipative non-equilibrium dynamics of a lower-dimensional auxiliary boundary field theory. We demonstrate that the spatial correlation…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
We prove a fluid limit for the coarsening phase of the condensing zero-range process on a finite number of sites. When time and occupation per site are linearly rescaled by the total number of particles, the evolution of the process is…
Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition…
The measurement process for hidden-configuration formulations of quantum mechanics is analysed. It is shown how a satisfactory description of quantum measurement can be given in this framework. The unified treatment of hidden-configuration…