Related papers: Polynomial escape rates via maximal large deviatio…
We prove a moderate deviation principle for the continuous time interpolation of discrete time recursive stochastic processes. The methods of proof are somewhat different from the corresponding large deviation result, and in particular the…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of memory loss. The maps may be chosen in any…
We prove the large deviations principle (LDP) for the law of the solutions to a class of semilinear stochastic partial differential equations driven by multiplicative noise. Our proof is based on the weak convergence approach and…
This paper introduces a versatile approach for computing the risk of collision specifically tailored for scenarios featuring low relative encounter velocities, but with potential applicability across a wide range of situations. The…
We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic max(min) polynomial equations, referred to as maxPPSs (and minPPSs, respectively), in time polynomial in both the encoding…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…
We study the computational complexity of decomposing finite discrete dynamical systems (FDDSs) in terms of the semiring operations of alternative and synchronous execution, which is useful for the analysis of discrete phenomena in science…
We have observed an interesting, yet unexplained, phenomenon: Semidefinite programming (SDP) based relaxations of maximum likelihood estimators (MLE) tend to be tight in recovery problems with noisy data, even when MLE cannot exactly…
Dynamical systems with components whose sizes evolve according to multiplicative stochastic rules have been recently combined with entry and exit processes. We show that the assumptions usually made in modeling exits are at odds with the…
We prove a large deviation principle for a greedy exploration process on an Erd\"os-R\'enyi (ER) graph when the number of nodes goes to infinity. To prove our main result, we use the general strategy to study large deviations of processes…
We revisit the finite time analysis of policy gradient methods in the one of the simplest settings: finite state and action MDPs with a policy class consisting of all stochastic policies and with exact gradient evaluations. There has been…
Computation of the interleaving distance between persistence modules is a central task in topological data analysis. For $1$-parameter persistence modules, thanks to the isometry theorem, this can be done by computing the bottleneck…
We obtain error rates for large deviations of sums of i.i.d. random variables in, a particular case, of the domain of a non-symmetric infinite mean $\alpha=1$-stable law. The focus of this work is on the method of proof via analytic…
In recent years there has been a growing interest in developing "streaming algorithms" for efficient processing and querying of continuous data streams. These algorithms seek to provide accurate results while minimizing the required storage…
This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the…
We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
In Large Language Model (LLM) inference, early-exit refers to stopping computation at an intermediate layer once the prediction is sufficiently confident, thereby reducing latency and cost. However, recent LLMs adopt improved pretraining…
The aim of this paper is to improve the large deviation principle for the number of descents in a random permutation by establishing a sharp large deviation principle of any order. We shall also prove a sharp large deviation principle of…