相关论文: Randomness as an Equilibrium. Potential and Probab…
The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment.…
A comprehensive new approach is presented for deriving probability densities of physical properties characterizing lens or source that constitute an observed galactic microlensing event. While previously encountered problems are overcome,…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
Strict frequentism defines probability as the limiting relative frequency in an infinite sequence. What if the limit does not exist? We present a broader theory, which is applicable also to random phenomena that exhibit diverging relative…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
We compute the uniform probability that finitely many polynomials over a finite field are pairwise coprime and compare the result with the formula one gets using the natural density as probability measure. It will turn out that the formulas…
It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes…
We calculate a collective number of thermodynamic quantities in a one-dimensional gas of hard elongated objects (such as needles) whose centers mobile on a line. Our formalism uses an approximation for the probabilities of contact between…
Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The…
We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly…
We consider two classes of probability distributions for configurations of the ideal gas. They depend only on kinetic energy and they remain of the same form when degrees of freedom are integrated out. The relation with equilibrium…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…
The Lorentz gas is one of the simplest, most widely used models to study the transport properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting point particles in an infinite array of fixed spherical…
In almost every scientific field, an experiment involves collecting data and then analysing it. The analysis stage will often consist in trying to extract some physical parameter and estimating its uncertainty; this is known as Parameter…
Boltzmann's Principle S = k ln W was repeatedly criticized by Einstein since it lacked a proper dynamical foundation in view of the thermal motion of the particles, out of which a physical system consists. This suggests, in particular, that…
The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.
Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$, a common…
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…