Related papers: A functional limit theorem for general shot noise …
We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a…
Coherent beam combining refers to the process of generating a bright output beam by merging independent input beams with locked relative phases. We report the first quantum mechanical noise limit calculations for coherent beam combining and…
We study the crossover between thermal and shot-noise power in a chaotic quantum dot in the presence of non-ideal contacts at finite temperature. The result explicitly demonstrates that the temperature affect the suppression-amplification…
Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural…
A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still…
Group synchronization refers to estimating a collection of group elements from the noisy pairwise measurements. Such a nonconvex problem has received much attention from numerous scientific fields including computer vision, robotics, and…
The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
We extend the statistical neurodynamics to study transient dynamics of sequence processing neural networks with finite dilution, and the theoretical results is supported by the extensive numerical simulations. It is found that the order…
Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…
We show that several general classes of stochastic processes satisfy a functional co-monotony principle, including processes with independent increments, Brownian diffusions, Liouville processes. As a first application, we recover some…
In this paper, we extend the central limit theorem of the additive functional of the nearest-neighbor zero-range process given in \cite{Quastel2002} to the long-range case. Our main results show that in several cases the limit processes are…
Here we review and extend central limit theorems for highly chaotic but deterministic semi-dynamical discrete time systems. We then apply these results show how Brownian motion-like results are recovered, and how an Ornstein-Uhlenbeck…
The quantum error-correcting code in the continuous-variable (CV) system attracts much attention due to its flexibility and high resistance against specific noise. However, the theory of fault tolerance in CV systems is premature and lacks…
A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. The averaged motion equation of the system with infinitely…
We construct $P(phi)_1$-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ…
We establish a sample path generation scheme in a unified manner for general multivariate infinitely divisible processes based on shot noise representation of their integrators. The approximation is derived from the decomposition of the…
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…
In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probability distribution: the so-called self-stabilizing processes.…
We study functions on the infinite-dimensional Hamming cube $\{-1,1\}^\infty$, in particular Boolean functions into $\{-1,1\}$, generalising results on analysis of Boolean functions on $\{-1,1\}^n$ for $n\in\mathbb{N}$. The notion of noise…