Related papers: Special invited paper. Large deviations
This is a lecture note produced for DS-GA 3001.003 "Special Topics in DS - Causal Inference in Machine Learning" at the Center for Data Science, New York University in Spring, 2024. This course was created to target master's and PhD level…
This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…
In this article for a finite typed random geometric graph we define the empirical locality distribution, which records the number of nodes of a given type linked to a given number of nodes of each type. We find large deviation principle…
Let $(X_t,t\geq 0)$ be a random walk on $\mathbb{Z}^d$. Let $ l_T(x)= \int_0^T \delta_x(X_s)ds$ the local time at the state $x$ and $ I_T= \sum\limits_{x\in\mathbb{Z}^d} l_T(x)^q $ the q-fold self-intersection local time (SILT). In…
We extend the study by Ornstein and Weiss on the asymptotic behavior of the normalized version of recurrence times and establish the large deviation property for a certain class of mixing processes. Further, an estimator for entropy based…
In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…
This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.
We examine various consequences of the existence of exceptional representations of an irreducible Weyl group. (These are notes from a talk in the MIT Lie groups seminar.)
We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…
Delays associated with elementary interaction processes are investigated. The case of broad resonances is discussed in the context of reaction simulations.
We establish a large deviation principle for time dependent trajectories (paths) of the empirical density of $N$ particles with long range interactions, for homogeneous systems. This result extends the classical kinetic theory that leads to…
This work is based on a bottom{-}up approach to the standard{-}model effective field theory (SMEFT), resulting in an equiprobable space of Wilson coefficients. The randomly generated Wilson coefficients of the SMEFT (in the Warsaw basis)…
These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…
A random variable is sampled from a discrete distribution. The missing mass is the probability of the set of points not observed in the sample. We sharpen and simplify McAllester and Ortiz's results (JMLR, 2003) bounding the probability of…
We extend classical results by A. V. Nagaev [Izv. Akad. Nauk UzSSR Ser. Fiz.--Mat. Nauk 6 (1969) 17--22, Theory Probab. Appl. 14 (1969) 51--64, 193--208] on large deviations for sums of i.i.d. regularly varying random variables to partial…
We study the large deviation estimates for the short time asymptotic behavior of a strongly degenerate diffusion process. Assuming a nilpotent structure of the Lie algebra generated by the driving vector fields, we obtain a graded large…
We define a special network that exhibits the large embeddings in any class of similar algebras. With the aid of this network, we introduce a notion of distance that conceivably counts the minimum number of dissimilarities, in a sense,…
In this talk, I summarize the status of our understanding of the puzzle of large gauge invariance at finite temperature.
We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…
These lecture notes were prepared for a special topics course in the Department of Statistics at the University of Washington, Seattle. They comprise the first eight chapters of a book currently in progress.