Related papers: On approximation by random L\"uroth expansions

For 0 < x < 1, take the binary expansion with infinitely many 0's, replace each 0 with -1, this gives the polarized binary expansion of x. Let R_i(x) be the ith "polarized bit" and let S_n(x) be the sum of the first n R_i(x). {S_n} is the…

We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress towards an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration…

We propose a randomized lattice algorithm for approximating multivariate periodic functions over the $d$-dimensional unit cube from the weighted Korobov space with mixed smoothness $\alpha > 1/2$ and product weights…

Let U be a given function defined on R^d and \pi(x) be a density function proportional to \exp -U(x). The following diffusion X(t) is often used to sample from \pi(x), dX(t)=-\nabla U(X(t)) dt+\sqrt2 dW(t),\qquad X(0)=x_0. To accelerate the…

We consider a Branching Random Walk on $\R$ whose step size decreases by a fixed factor, $0<b<1$, with each turn. This process generates a random probability measure on $\R$, that is, the limit of uniform distribution among the $2^n$…

This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue…

We introduce a novel family of expander-based error correcting codes. These codes can be sampled with randomness linear in the block-length, and achieve list-decoding capacity (among other local properties). Our expander-based codes can be…

We prove $L^p$ boundedness results, $p > 2$, for local maximal averaging operators over a smooth 2D hypersurface $S$ with either a $C^1$ density function or a density function with a singularity that grows as $|(x,y)|^{-\beta}$ for $\beta <…

This paper studies the expected $L_p$-discrepancy ($2 \leq p < \infty$) for stratified sampling schemes under importance sampling. We introduce a parametric family of equivolume partitions $\Omega_{\theta,\sim}$ and leverage recent exact…

We establish sharp estimates for the convergence rate of the Kranosel'ski\v{\i}-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of…

This paper shows the convergence of adele-valued random walks to an adelic L\'evy process under scaling limits. We use random walks on the $p$-adic numbers to construct random walks initially on the infinite product space, and use survival…

We establish stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota-Yorke maps under a variety of perturbations. Our family of random maps need not be close to a fixed map; thus, our results can…

Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…

We propose a novel method for establishing the sparsity of the coefficients of the Laguerre generalized polynomial chaos expansion of solutions to parametric elliptic PDEs with log-gamma inputs on $\mathbb{R}_+^\infty$. The established…

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…

Sampling a random permutation with restricted positions, or equivalently approximating the permanent of a 0-1 matrix, is a fundamental problem in computer science, with several notable results achieved over the years. However, existing…

We present an explicit construction of a Markovian random growth process on integer partitions such that given it visits some level $n$, it passes through any partition $\lambda$ of $n$ with equal probabilities. The construction has…

Given a graph $G$ and $p\in [0,1]$, the random subgraph $G_p$ is obtained by retaining each edge of $G$ independently with probability $p$. We show that for every $\epsilon>0$, there exists a constant $C>0$ such that the following holds.…

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…

In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation…