Related papers: Fluctuations of Schensted row insertion
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
Stochastic embedding transitions introduce a probabilistic mechanism for adjusting token representations dynamically during inference, mitigating the constraints imposed through static or deterministic embeddings. A transition framework was…
In [O'Connell and Yor (2002)] a path-transformation G was introduced with the property that, for X belonging to a certain class of random walks on the integer lattice, the transformed walk G(X) has the same law as that of the original walk…
We introduce an object called a decorated Young tableau which can equivalently be viewed as a continuous time trajectory of Young diagrams or as a non-intersecting line ensemble. By a natural extension of the Robinson-Schensted…
We study numerically the correlations and the distribution of intervals between successive zeros in the fluctuating geometry of stochastic interfaces, described by the Edwards-Wilkinson equation. For equilibrium states we find that the…
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…
By random complex zeroes we mean the zero set of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!. This zero set is distribution invariant…
Notes from a course at the ATM Workshop on Schubert Varieties, held at The Institute of Mathematical Sciences, Chennai, in November 2017. Various expansions of Schur functions, the Lindstr\"om-Gessel-Viennot lemma, semistandard Young…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
We study an infinite version of the "jeu de taquin" sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods…
Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L)…
Given a permutation $\sigma$, the Robinson-Schensted correspondence determines a certain partition called the shape of $\sigma$. Famously, the shape measures the longest unions of increasing and decreasing subsequences, thus giving global…
Random $s$-intersection graphs have recently received considerable attention in a wide range of application areas. In such a graph, each vertex is equipped with a set of items in some random manner, and any two vertices establish an…
A central limit theorem is shown for moderately interacting particles in the whole space. The interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb type. It is proved that the fluctuations become…
The Berele row-insertion is a symplectic analogue of the Schensted row-insertion. In the present paper, we provide it with a representation theoretical interpretation via the quantum symmetric pairs of type $A\mathrm{II}$. As applications,…
Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…
If a partition $\lambda$ of size n is chosen randomly according to the Plancherel measure $P_n[\lambda] = (\dim \lambda)^2/n!$, then as n goes to infinity, the rescaled shape of $\lambda$ is with high probability very close to a non-random…
Invariant ensemble, which are characterised by the joint distribution of eigenvalues $P(\lambda_1,\ldots,\lambda_N)$, play a central role in random matrix theory. We consider the truncated linear statistics $L_K = \sum_{n=1}^K f(\lambda_n)$…
Large vacuum fluctuations of a quantum stress tensor operator can be described by the asymptotic behavior of the probability distribution of the time or spacetime averaged operator. Here we focus on the case of stress tensor operators…
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…