Related papers: Complexity is not Enough for Randomness
Stochastic homogenization is achieved for a class of elliptic and parabolic equations describing the lifetime, in large domains, of stationary diffusion processes in random environment which are small, statistically isotropic perturbations…
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such…
We consider the bias arising from time discretization when estimating the threshold crossing probability $w(b) := \mathbb{P}(\sup_{t\in[0,1]} B_t > b)$, with $(B_t)_{t\in[0,1]}$ a standard Brownian Motion. We prove that if the…
We consider a closed macroscopic quantum system in a pure state $\psi_t$ evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces $\mathcal{H}_\nu$ (macro spaces) of Hilbert space, each…
We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-complexity grows linearly before saturating at a late-time value of…
We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In random dynamical system, this indicator coincides with the rate K of divergence of…
A non-vanishing entropy production rate is one of the defining characteristics of any non-equilibrium system, and several techniques exist to determine this quantity directly from experimental data. The short-time inference scheme, derived…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
The circuit complexity of time-evolved pure quantum states grows linearly in time for an exponentially long time. This behavior has been proven in certain models, is conjectured to hold for generic quantum many-body systems, and is believed…
We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the…
Let $W^H=\{W^H(t), t \in \rr\}$ be a fractional Brownian motion of Hurst index $H \in (0, 1)$ with values in $\rr$, and let $L = \{L_t, t \ge 0\}$ be the local time process at zero of a strictly stable L\'evy process $X=\{X_t, t \ge 0\}$ of…
We study a model of interacting random walkers that proposes a simple mechanism for the emergence of cooperation in group of individuals. Each individual, represented by a Brownian particle, experiences an interaction produced by the local…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. On many occasions it is possible to approach the problem by performing an appropriate decomposition into a bath and…
How much does local and time-periodic dynamics resemble a random unitary? In the present work we address this question by using the Clifford formalism from quantum computation. We analyse a Floquet model with disorder, characterised by a…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…
Quantum entanglement is considered, by and large, to be a very delicate and non-robust phenomenon that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest…
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase in the number of parameters with system size and experimental imperfections, this…