Related papers: Sawtooth models and asymptotic independence in lar…

This is an expanded version of lectures given in Hangzhou and Beijing, on the symplectic forms common to Seiberg-Witten theory and the theory of solitons. Methods for evaluating the prepotential are discussed. The construction of new…

Normalized random measures with independent increments represent a large class of Bayesian nonaprametric priors and are widely used in the Bayesian nonparametric framework. In this paper, we provide the posterior consistency analysis for…

For $\widetilde{\cal R} = 1 - \exp(- {\cal R})$ a random closed set obtained by exponential transformation of the closed range ${\cal R}$ of a subordinator, a regenerative composition of generic positive integer $n$ is defined by recording…

We construct "connected" (0,2) sigma models starting from n copies of (2,2) CP(N-1) models. General aspects of models of this type (known as T+O deformations) had been previously studied in the context of heterotic string theories. Our…

We prove limit theorems for the number of fixed points, descents, and inversions of iterated random-to-top shuffles in two asymptotic regimes. Our proofs are analytic, and they utilize new combinatorial decompositions that represent each…

This paper deals with a general class of transformation models that contains many important semiparametric regression models as special cases. It develops a self-induced smoothing for the maximum rank correlation estimator, resulting in…

Let either $X=\mathbf{R}\times\mathbf{T}$ or $X=\Sigma_\text{\boldmath $a$}\times\mathbf{T}$, where $\mathbf{R}$ is the additive group of real number, $\mathbf{T}$ is the cycle group and $\Sigma_\text{\boldmath $a$}$ is an $\text{\boldmath…

Let $\sigma_t(x)$ denote the implied volatility at maturity $t$ for a strike $K=S_0 e^{xt}$, where $x\in\bbR$ and $S_0$ is the current value of the underlying. We show that $\sigma_t(x)$ has a uniform (in $x$) limit as maturity $t$ tends to…

We introduce the first random matrix model of a complex $\beta$-ensemble. The matrices are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite $\beta$-ensembles discovered by Dumitriu and Edelman (J. Math. Phys.,…

Recently a class of generalized information measures was defined on sets of items parametrized by submodular functions. In this paper, we propose and study various notions of independence between sets with respect to such information…

Let $S_n$ be the symmetric group on the set $\{1,2,\ldots,n\}$. Given a permutation $\sigma=\sigma_1\sigma_2 \cdots \sigma_n \in S_n$, we say it has a peak at index $i$ if $\sigma_{i-1}<\sigma_i>\sigma_{i+1}$. Let $\text{Peak}(\sigma)$ be…

In this article, the notion of bi-monotonic independence is introduced as an extension of monotonic independence to the two-faced framework for a family of pairs of algebras in a non-commutative space. The associated cumulants are defined…

The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…

We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in…

We study pairs and m--tuples of compositions of a positive integer n with parts restricted to a subset P of positive integers. We obtain some exact enumeration results for the number of tuples of such compositions having the same number of…

For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…

In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can…

We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…

A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…

Under the assumption that the distribution of a nonnegative random variable $X$ admits a bounded coupling with its size biased version, we prove simple and strong concentration bounds. In particular the upper tail probability is shown to…