相关论文: Complexity is not Enough for Randomness
Human-created engines and evolutionarily optimized molecular motors exhibit sophisticated design in order to harvest chemical or thermal energy for generating unidirectional motion. The complexity of these motors makes their random…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
We propose new analytical tools for describing growth-rate distributions generated by stationary time-series. Our analysis shows how deviations from normality are not pathological behaviour, as suggested by some traditional views, but…
Continuity of local time for Brownian motion ranks among the most notable mathematical results in the theory of stochastic processes. This article addresses its implications from the point of view of applications. In particular an extension…
Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of random quantum circuits with a specific gate structure. Within this framework, we…
A major line of questions in quantum information and computing asks how quickly locally random circuits converge to resemble global randomness. In particular, approximate k-designs are random unitary ensembles that resemble random circuits…
We study the fluctuation properties of the local time density, ${\rho _T} = \frac{1}{T}\int_0^T {\delta ( {r(t) - 1} )} dt$, spent by a $d$-dimensional Brownian particle at a spherical shell of unit radius, where $r(t)$ denotes the radial…
What is the relationship between the complexity of a learner and the randomness of his mistakes? This question was posed in \cite{rat0903} who showed that the more complex the learner the higher the possibility that his mistakes deviate…
We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined as the continuous dependence of the…
It is well-known that the height profile of a critical conditioned Galton-Watson tree with finite offspring variance converges, after a suitable normalization, to the local time of a standard Brownian excursion. In this work, we study the…
We consider a system of non-interacting Brownian particles on a line with a step-like initial condition, and we investigate the behavior of the local time at the origin at large times. We compute the mean and the variance of the local time,…
The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve.…
Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species.…
The ability to produce random numbers that are unknown to any outside party is crucial for many applications. Device-independent randomness generation does not require trusted devices and therefore provides strong guarantees of the security…
In this paper we study the local times of Brownian motion from the point of view of algorithmic randomness. We introduce the notion of effective local time and show that any path which is Martin-L\"of random with respect to the Wiener…
We explore the relationship between complexity and duality in quantum systems, focusing on how local and non-local operators evolve under time evolution. We find that non-local operators, which are dual to local operators under specific…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
We prove a new concentration result for non-catalytic decoupling by showing that, for suitably large $t$, applying a unitary chosen uniformly at random from an approximate $t$-design on a quantum system followed by a fixed quantum operation…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
Robustness, the ability of a system to maintain performance under significant and unanticipated environmental changes, is a critical property for robotic systems. While biological systems naturally exhibit robustness, there is no…