相关论文: Random Feedback Shift Registers, and the Limit Dis…

A comment on the Letter by Le Doussal and Wiese, Phys. Rev. Lett. 96, 197202 (2006).

These notes describe several loop soup models and their {\it universal behaviour} in dimensions greater or equal to 3. These loop models represent certain classical or quantum statistical mechanical systems. These systems undergo phase…

Given two equally long, uniformly random binary strings, the expected length of their longest common subsequence (LCS) is asymptotically proportional to the strings' length. Finding the proportionality coefficient $\gamma$, i.e. the limit…

We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…

The transmission (T) and reflection (R) coefficients are studied in periodic systems and random systems with gain. For both the periodic electronic tight-binding model and the periodic classical many-layered model, we obtain numerically and…

Feller (1945) provided a coupling between the counts of cycles of various sizes in a uniform random permutation of $[n]$ and the spacings between successes in a sequence of $n$ independent Bernoulli trials with success probability $1/n$ at…

The Poisson--Dirichlet distribution arises in many different areas. The parameter $\theta$ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of $\theta$ approaching…

Single index linear models for binary response with random coefficients have been extensively employed in many econometric settings under various parametric specifications of the distribution of the random coefficients. Nonparametric…

If we treat the symmetric group $S_n$ as a probability measure space where each element has measure $1/n!$, then the number of cycles in a permutation becomes a random variable. The Cycle Length Lemma describes the expected values of…

Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…

Selecting N random points in a unit square corresponds to selecting a random permutation. By putting 5 types of symmetry restrictions on the points, we obtain subsets of permutations : involutions, signed permutations and signed…

We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first for which the critical probability p_c \ne 1/2.…

Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary…

In this paper we consider a random walk of a particle in $\mathbb{R}^d$. Convergence of different transformations of trajectories of random flights with Poisson switching moments has been obtained by Davydov and Konakov, as well as…

The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…

We define a generalized Golomb--Dickman constant $\lambda_{\theta}$ as the limiting expected proportion of the longest cycle in random permutations under the Ewens measure with parameter $\theta > 0$. Exploiting the independence properties…

We investigate a model of random spatial permutations on two-dimensional tori, and establish that the joint distribution of large cycles is asymptotically given by the Poisson--Dirichlet distribution with parameter one. The asymmetry of the…

By deriving a general expression for multiplicity distribution (a conditional probability distribution) in statistical model, we demonstrate the mismatches between experimental measurements and previous theoretical calculations on…

We study the reknown deconvolution problem of recovering a distribution function from independent replicates (signal) additively contaminated with random errors (noise), whose distribution is known. We investigate whether a Bayesian…

We present a new proof of a fundamental result concerning cycles of random permutations which gives some intuition for the connection between Touchard polynomials and the Poisson distribution. We also introduce a rather novel permutation…