Related papers: Notes on switching lemmas

We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution…

We formalize various counting principles and compare their strengths over $V^{0}$. In particular, we conjecture the following mutual independence between: (1) a uniform version of modular counting principles and the pigeonhole principle for…

In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.

Motivated by the Beck-Fiala conjecture, we study discrepancy bounds for random sparse set systems. Concretely, these are set systems $(X,\Sigma)$, where each element $x \in X$ lies in $t$ randomly selected sets of $\Sigma$, where $t$ is an…

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…

Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…

It has been widely acknowledged that probabilistic independence and logical independence cannot be coherently reconciled. By bridging these two notions, this paper addresses three long-standing problems that have puzzled the field of…

Duda, Hart, and Nilsson have set forth a method for rule-based inference systems to use in updating the probabilities of hypotheses on the basis of multiple items of new evidence. Pednault, Zucker, and Muresan claimed to give conditions…

Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…

We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…

Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…

In this paper we present the result of successively applying a Chebyshev polynomial to a continuous random variable. In particular we show that under mild assumptions the limiting distribution will be the same as the weight with respect to…

Let $ V_{n} = X_{1,n} + X_{2,n} + \cdots + X_{n,n}$ where $X_{i,n}$ are Bernoulli random variables which take the value $1$ with probability $b(i;n)$. Let $\lambda_{n} = \sum\limits_{i=1}^{n} b(i;n) $, $\lambda = \lim\limits_{n \to \infty}…

Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…

A Central Limit Theorem for non-commutative random variables is proved using the Lindeberg method. The theorem is a generalization of the Central Limit Theorem for free random variables proved by Voiculescu. The Central Limit Theorem in…

A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete…

We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

Pick $N$ random points $U_1,\cdots,U_{N}$ independently and uniformly in a triangle ABC with area 1, and take the convex hull of the set $\{A,B,U_1,\cdots,U_{N}\}$. The boundary of this convex hull is a convex chain $V_0=B,V_1,\cdots,$…