"... treating the cumulants as elements of the polynomial ring."

I guess I'll be TAing it this semester.

"It is shown that at least 50% of the probability mass of a sum of independent Rademacher random variables is within one standard deviation from its mean. This lower bound is sharp, it is much better than for instance the bound that can be obtained from application of the Chebishev inequality..."

"An alternate form for the binomial tail is presented, which leads to a variety of bounds for the central tail. A few can be weakened into the corresponding Chernoff and Slud bounds, which not only demonstrates the quality of the presented bounds, but also provides alternate proofs for the classical bounds."

"Let $P$ be a probability distribution on $q$-dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension $d << q$, most $d$-dimensional projections of $P$ look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension $q$. It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting $\hat{P}$ be the empirical distribution of $n$ independent random vectors with distribution $P$, we investigate the behavior of the empirical process $\sqrt{n}(\hat{P} - P)$ under random projections, conditional on $\hat{P}$."

"Uniform probability distributions on $\ell_p$ balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a simplex and a sphere. Certain new and interesting features, such as phase transitions and localization phenomena emerge."

Upon a uniform RV, compute an "$\alpha-local$" or decision forest function upon it. By doing so, you can't get particularly close to the uniform or "majmod" output distribution. Utilizes an anti-concentration result from 1943.

"We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar “conventional” probability calculus and always retains the latter as a special case when all matrices are diagonal."

One needs the densities to use the likelihood ratio, so what's the point of these bounds?

"...the Lambert W approach allows practicioners to "Gaussianize" their heavy-tailed data and apply common methods and models on the latent Gaussian RV. The optimal parameters to do the backtransformation can be estimated by maximum likelihood (ML). Contrary to the skewed case, the transformation is bijective: each observed data point is uniquely linked to its hidden (and normally tailed) input."

"This work is an attempt to lay new foundations for probability theory, using a tiny bit of nonstandard analysis."

"In this paper we prove a weighted version of the Khintchine inequalities."

A sharp lower bound for the maximal probability.

An extension theorem for exchangeable sequences.

Also see the upcoming paper "On the computability of conditional probability".

Derivation and application of a theorem which is a bit more usable than Sourav's original result.

"This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with other functional inequalities and also large deviation theory."

"We consider the problem of modifying a quasi-probability kernel in order to improve its properties without changing the set of measures whose conditional probabilities it specifies."

A density-like concept "defined in terms of the average value of the logarithms of the densities of the distributions of principal components for a given dimension", along with an estimation method.

A very nice course project by an old TA which summarizes Mossel's "Gaussian bounds for noise correlations and tight analysis of long codes" and applies it to a sensitivity problem.

This year and onwards: less stochastic calculus, more empirical processes.

Lots of these have already been posted on arXiv.

A technique of replacing non-Gaussian random variables with Gaussian ones, recently utilized by Tao and Vu to prove a property about Wigner Hermitian matrices.

Workshop at Texas A&M.

With a nice story about (fallacious) statistical perception.

Short proof of a restricted version.

Symbolic definition of independence as the basis of a symbolic model for partial information leakage.

"Mathematical probability can be based on a two-person sequential game of perfect information. On each round, Player II states odds at which Player I may bet on what Player II will do next. In statistical modeling, Player I is a statistician and Player II is the world. In finance, Player I is an investor and Player II is a market."

"The Art of the Probable" addresses the history of scientific ideas, in particular the emergence and development of mathematical probability. But it is neither meant to be a history of the exact sciences per se nor an annex to, say, the Course 6 curriculum in probability and statistics. Rather, our objective is to focus on the formal, thematic, and rhetorical features that imaginative literature shares with texts in the history of probability. These shared issues include (but are not limited to): the attempt to quantify or otherwise explain the presence of chance, risk, and contingency in everyday life; the deduction of causes for phenomena that are knowable only in their effects; and, above all, the question of what it means to think and act rationally in an uncertain world."

"Cuckoo hashing provides a useful methodology for building practical, high-performance hash tables. The essential idea of cuckoo hashing is to combine the power of schemes that allow multiple hash locations for an item with the power to dynamically change the location of an item among its possible locations. Previous work on the case where the number of choices is larger than two has required a breadth-first search analysis, which is both inefficient in practice and currently has only a polynomial high probability upper bound on the insertion time. Here we signicantly advance the state of the art by proving a polylogarithmic bound on the more efficient randomwalk method, where items repeatedly kick out random blocking items until a free location for an item is found."

Pick up a copy of van der Vaart.

Don't say squaring. Given an algorithm D that distinguishes ensembles X and Y indexed by α, this is a BPP algorithm D' such that ℙ(D'(α, X)=1) - ℙ(D'(α, Y)=1) ≥ ρ(ℙ(D(α, X)=1) - ℙ(D(α, Y)=1)|) for some ρ.

I was afraid they were actually going to blame the credit collapse on a representation of a multivariate distribution. Instead they blamed the practitioners and slapped on a dumb headline.

"This book presents an approach to large deviation theory which is based on evaluating the asymptotics of certain expectations."