相关论文: The probability of the Alabama paradox
We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable {\epsilon}-transitions (also called null transitions), allowing state…
The Herman Protocol Conjecture states that the expected time $\mathbb{E}(\mathbf{T})$ of Herman's self-stabilizing algorithm in a system consisting of $N$ identical processes organized in a ring holding several tokens is at most…
An integer partition of $n$ is a decreasing sequence of positive integers that add up to $[n]$. Back in $1979$ Macdonald posed a question about the limit value of the probability that two partitions chosen uniformly at random, and…
In a compound decision problem, consisting of $n$ statistically independent copies of the same problem to be solved under the sum of the individual losses, any reasonable compound decision rule $\delta$ satisfies a natural symmetry…
In the critical beta-splitting model of a random $n$-leaf binary tree, leaf-sets are recursively split into subsets, and a set of $m$ leaves is split into subsets containing $i$ and $m-i$ leaves with probabilities proportional to…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set.…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is…
Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…
Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be…
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with…
The tacnode process is a universal determinantal point process arising from non-intersecting particle systems and tiling problems. It is the aim of this work to explore the integrable structure and large gap asymptotics for the gap…
We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the…
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…
We revisit the problem of influencing the sex ratio of a population by subjecting reproduction of each family to some stopping rule. As an easy consequence of the strong law of large numbers, no such modification is possible in the sense…
This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irreducible parts, where irreducibility is understood in terms…
A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…
We introduce a sieve for counting twin primes up to a given range. Our method depends on a parameter ${\lambda}_x$ and the estimation of the number of twin primes obtained as a result, is called a fundamental structure of the distribution…