Related papers: A Theorem of Probability
I present a simple derivation of the de Gennes narrowing phenomenon.
We prove Union-Closed sets conjecture.
We here put forward a simple argument for Born's rule based on the requirement that the probability distribution should not be a function of the number of degrees of freedom.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
Vapnik--Chervonenkis' theorem is a seminal result in machine learning. It establishes sufficient conditions for empirical probabilities to converge to theoretical probabilities, uniformly over families of events. It also provides an…
We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.
The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so; it…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
We give a simple non-analytic proof of Biggins' theorem on martingale convergence for branching random walks.
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
An s-tuple of positive integers are k-wise relatively prime if any k of them are relatively prime. Exact formula is obtained for the probability that s positive integers are k-wise relatively prime.
In this paper we show an index theorem for gerbes
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
By using the strong approximation, this paper establishes several limit results on the convergent rate of a infinite series of probabilities on the other law of iterated logarithm.
An approximate formula for the partitions of Goldbach's Conjecture is derived using Prime Number Theorem and a heuristic probabilistic approach. A strong form of Goldbach's conjecture follows in the form of a lower bounding function for the…
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
Here I discuss ideas that makes a synthesis of topology and probability theory. The idea is the following: given a set $X$, assign a number $p(A)\in [0,1]$ for any subset $A$ of $X$. We can interpret $p(A)$ as the probability of openness of…