Related papers: Universal limits of nonlinear measure redistributi…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
We consider a free fermion chain with uniform nearest-neighbor hopping and let it evolve from an arbitrary initial state with a fixed macroscopic number of particles. We then prove that, at a sufficiently large and typical time, the…
This paper studies the propagation of finite-sample uncertainty under nonlinear transformations commonly used in statistical decision systems. In particular, we consider process capability indices, which are widely used in manufacturing…
We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the…
Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all…
The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered.…
In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…
Although the laws of classical physics are deterministic, thermodynamics gives rise to an arrow of time through irreversible processes. In quantum mechanics the unitary nature of the time evolution makes it intrinsically reversible, however…
The problem of a massive elastic string depinning from a linear defect under the action of a small driving force is considered. To exponential accuracy the decay rate is calculated with the help of the instanton method; then, fluctuations…
Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discon- tinuous derivative can generate multiple…
Time evolution of a perturbed thermal state is studied in a quantum-mechanical system with O(N) symmetry. In the limit of large N, time dependence of O(N)-singlet expectation values can be described by classical equations of motion in a…
Time dependent signals in experimental techniques such as Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an ensemble average over many microscopical dynamical processes. While there are a number of…
We develop a systematic, omnibus approach to goodness-of-fit testing for parametric distributional models when the variable of interest is only partially observed due to censoring and/or truncation. In many such designs, tests based on the…
Polynomial time reductions between problems have long been used to delineate problem classes. Simulation reductions also exist, where an oracle for simulation from some probability distribution can be employed together with an oracle for…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal…
We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which…
Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes…
What is the probability that all the gas in a box accumulates in the same half of this box? Though amusing, this question underlies the fundamental problem of density fluctuations at equilibrium, which has profound implementations in many…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…