Related papers: An introduction to the probabilistic method throug…

These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…

Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…

We define criteria for a hidden variables theory to be Lorentz invariant and prove that it implies no signaling. As a result, we show that a Lorentz invariant and contextual theory (e.g., quantum field theory) must be genuinely stochastic,…

While there has been significant progress on algorithmic aspects of the Lov\'{a}sz Local Lemma (LLL) in recent years, a noteworthy exception is when the LLL is used in the context of random permutations. The breakthrough algorithm of Moser…

Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the…

In a finite volume system, we prove a no-go theorem on a Leibniz rule with a care of locality argument on latttice. The new possibility on the Leibniz rule solutions on lattice is discussed. Although the new solution admits a local…

In this paper, we obtain a local limit theorem for the Kemperman's model of oscillating random walk on $\mathbb{Z}$; it extends the existing results for classical random walks on $\mathbb Z$ or reflected random walks on $\mathbb N_0$. The…

We give a lower bound on the growth of a subshift based on a simple condition on the set of forbidden patterns defining that subshift. Aubrun et Al. showed a similar result based on the Lov\'asz Local Lemma for subshift over any countable…

In complex Langevin simulations, the insufficient decay of the probability density near infinity leads to boundary terms that spoil the formal argument for correctness. We present a formulation of this term that is cheaply measurable in…

We study the computational power of randomized computations on infinite objects, such as real numbers. In particular, we introduce the concept of a Las Vegas computable multi-valued function, which is a function that can be computed on a…

We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give…

In this paper, lower bounds on the probability of a finite union of events are considered, i.e. $P\left(\bigcup_{i=1}^N A_i\right)$, in terms of the individual event probabilities $\{P(A_i), i=1,\ldots,N\}$ and the sums of the pairwise…

To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

In probabilistic approaches to classification and information extraction, one typically builds a statistical model of words under the assumption that future data will exhibit the same regularities as the training data. In many data sets,…

The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…

The sequence of $\alpha$-trimmings of empirical probabilities is shown to converge, in the Painlev\'{e}--Kuratowski sense, on the class of probability measures endowed with the weak topology, to the $\alpha$-trimming of the population…

This is an exposition of the contributions of L\'aszl\'o Lov\'asz to mathematics and computer science written on the occasion of the bestowal of the Abel Prize~2021 to him. Our survey, of course, cannot be exhaustive. We sketch remarkable…

By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…