Related papers: Local tail bounds for polynomials on the discrete …

We derive simple but nearly tight upper and lower bounds for the binomial lower tail probability (with straightforward generalization to the upper tail probability) that apply to the whole parameter regime. These bounds are easy to compute…

We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials

While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…

In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…

Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.

We provide finite sample upper and lower bounds on the Binomial tail probability which are a direct application of Sanov's theorem. We then use these to obtain high probability upper and lower bounds on the minimum of i.i.d. Binomial random…

For an integral convex polytope $\mathcal{P} \subset \mathbb{R}^d$, we recall $L_\mathcal{P}(n)=|n\mathcal{P} \cap \mathbb{Z}^d|$ the Ehrhart polynomial of $\mathcal{P}$. Let $g_r(\mathcal{P})$ be the $r$th coefficients of…

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…

We prove a quantitative version of the bound on the smallest singular value of a Bernoulli covariance matrix (due to Bai and Yin). Then we use this bound, together with several recent developments, to show that the distance from a random…

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…

We re-examine a lower-tail upper bound for the random variable $$X=\prod_{i=1}^{\infty}\min\left\{\sum_{k=1}^iE_k,1\right\},$$ where $E_1,E_2,\ldots\stackrel{iid}\sim\text{Exp}(1)$. This bound has found use in root-finding and seed-finding…

We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.

We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…

We derive upper bounds for probabilities of the form $P(g(\mathbf{X})\geq t)$ using the southwest boundary (recently introduced in our previous work) $\partial_{\mathrm{SW}} Q(g^{-1}[t,\infty))$, where $Q$ is a reflection to the first…

In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower…

We prove upper bounds on the transition probabilities of random walks with i.i.d. random conductances with a polynomial lower tail near $0$. We consider both constant and variable speed models. Our estimates are sharp. As a consequence, we…

We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.

Given a polynomial P in several variables over an algebraically closed field, we show that except in some special cases that we fully describe, if one coefficient is allowed to vary, then the polynomial is irreducible for all but at most…

It is shown that functions defined on $\{0,1,...,r-1\}^n$ satisfying certain conditions of bounded differences that guarantee sub-Gaussian tail behavior also satisfy a much stronger ``local'' sub-Gaussian property. For self-bounding and…