Related papers: New probability distribution describing emergence …
The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…
A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy,…
What can one say on convergence to stationarity of a finite state Markov chain that behaves "locally" like a nearest neighbor random walk on ${\mathbb Z}$ ? The model we consider is a version of nearest neighbor lazy random walk on the…
Choosing four entangled stets to form an orthogonal and complete basis for a two-particle system, we argue that a local hidden variable model should give the probability of each entangled state if the two-particle system is described by a…
We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of…
We study non-equilibrium models comprising of beads connected by springs. The system is coupled to two thermal baths kept at different temperatures. We derive the steady state probability distributions of positions of the bead for the…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
We enumerate arrangements of $n$ couples, i.e. pairs of people, placed in a single-file queue, and consider four statistics from the vantage point of a distinguished given couple. In how many arrangements are exactly $p$ of the $n-1$ other…
We have been investigating the problem of the Anderson localization in a disordered one dimensional tight-binding model. The disorder is created by the interaction of mobile particles with other species, immobilized at random positions. We…
From a new class of q-deformed coherent states we introduce a generalization of the Euler probability distribution for which the main statistical parameters are obtained explicitly. As application, we discuss the corresponding photon…
We derive a simple expression for the probability of trajectories of a master equation. The expression is particularly useful when the number of states is small and permits the calculation of observables that can be defined as functionals…
The notion of "paired" fermions is central to important condensed matter phenomena such as superconductivity and superfluidity. While the concept is widely used and its physical meaning is clear there exists no systematic and mathematical…
Consider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn…
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…
Multi-state models are commonly used for intermittent observations of a state over time, but these are generally based on the Markov assumption, that transition rates are independent of the time spent in current and previous states. In a…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
Entangled states are notoriously non-separable, their sub-ensembles being only statistical mixtures yielding no coherences and no quantum interference phenomena. The interesting features of entangled states can be revealed only by…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
Multiplicity distributions of neutral and charged particles arising from squeezed coherent states are investigated. Projections onto global isospin states are considered. We show how a small amount of squeezing can significantly change the…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…