Related papers: A distribution on triples with maximum entropy mar…

$S \subseteq \mathbb{Z}_{2n}$ is said to be sum-free if $S$ has no solution to the equation $a+b=c$. The sum-free process on $\mathbb{Z}_{2n}$ starts with $S:=\emptyset$, and iteratively inserts elements of $\mathbb{Z}_{2n}$, where each…

A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…

We give a new proof of Hilbert's Syzygy Theorem for monomial ideals. In addition, we prove the following. If S=k[x_1,...,x_n] is a polynomial ring over a field, M is a squarefree monomial ideal in S, and each minimal generator of M has…

The Principle of Maximum Entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive…

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…

A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of…

We study the root distribution of a sequence of polynomials $\{P_n(z)\}_{n=0}^{\infty}$ with the rational generating function $$ \sum_{n=0}^{\infty} P_n(z)t^n= \frac{1}{1+ B(z)t^\ell +A(z)t^k}$$ for $(k,\ell)=(3,2)$ and $(4,3)$ where $A(z)$…

A seminal result of Koml\'os, S\'ark\"ozy, and Szemer\'edi states that any n-vertex graph G with minimum degree at least (1/2 + {\alpha})n contains every n-vertex tree T of bounded degree. Recently, Pham, Sah, Sawhney, and Simkin extended…

In this short note, we extend the celebrated results of Tao and Vu, and Krishnapur on the universality of empirical spectral distributions to a wide class of inhomogeneous complex random matrices, by showing that a technical and…

Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…

A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally…

Let $\mu_1 \ge \dotsc \ge \mu_n > 0$ and $\mu_1 + \dotsm + \mu_n = 1$. Let $X_1, \dotsc, X_n$ be independent non-negative random variables with $EX_1 = \dotsc = EX_n = 1$, and let $Z = \sum_{i=1}^n \mu_i X_i$. Let $M = \max_{1 \le i \le n}…

When estimating a proportion and only a sample of triplets is given, dependencies within the triplets are to be accounted for. Without assuming a distribution for the success count of the triplet, together with the proportion, as second and…

In this paper, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advantages of…

In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the…

Let $L_n(k)$ denote the least common multiple of $k$ independent random integers uniformly chosen in $\{1,2,\ldots ,n\}$. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as…

Let $A^{(n)}_{l;k}\subset S_n$ denote the event that the set of $l$ consecutive numbers $\{k,k+1,\cdots, k+l-1\}$ appear in a set of $l$ consecutive positions. Let $p=\{p_j\}_{j=1}^\infty$ be a distribution on $\mathbb{N}$ with $p_j>0$. Let…

In this paper, we introduce a new distribution called Burr III-Weibull(BW) distribution using the concept of competing risk. We derive moments, conditional moments, mean deviation and quantiles of the proposed distribution. Also the Renyi's…

We count the ordered sum-free triplets of subsets in the group $\mathbb{Z}/p\mathbb{Z}$, i.e., the triplets $(A,B,C)$ of sets $A,B,C \subset \mathbb{Z}/p\mathbb{Z}$ for which the equation $a+b=c$ has no solution with $a\in A$, $b \in B$ and…

Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…