Related papers: Typical = random
The concept of a random Lagrangian is proposed. It is considered as a basis for a new view of the old problems such as renormalization, nonzero vacuum energy and the anthropic principle. It gives rise to nontrivial consequences both in…
The review paper presents generalization of d'Alembert's variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
The definition of conditional probability in case of continuous distributions was an important step in the development of mathematical theory of probabilities. How can we define this notion in algorithmic probability theory? In this survey…
We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. If we consider a conception of…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
This paper is a comment on the paper "Quantum Mechanics and Algorithmic Randomness" was written by Ulvi Yurtsever \cite{Yurtsever} and the briefly explanation of the algorithmic randomness of quantum measurements results. There are…