SOURAV CHATTERJEE THESIS

SOURAV CHATTERJEE THESIS

Theory Related Fields , , , We introduce two QMC constructions in the triangle with a vanishing discrepancy. Besides, we introduce two new directions by making use of zero biasing and equilibrium couplings. Since products of simplices is throughout of special interest to us, we end the dissertation with few results of QMC tractability on that domain. Stein’s method is a technique in probability theory introduced by Charles Stein in that enables one to obtain convergence rates in distributional approximations. Log in Favorites Help.

The material is accessible to anyone who has attended a graduate course in probability. The method makes use of characterizing differential equations of distributions and various coupling constructions to get error bounds with respect to certain probability metrics. Our result adds to an overall picture of the behavior of superconcentrated Gaussian processes described by Chatterjee. A two-dimensional shear lag model is developed to establish the important design parameters governing the formation of wrinkles. The first is a version of the van der Corput sequence customized to the unit triangle. Electronically uploaded by the author.

These point sets are much more uniformly distributed than random samples.

Finally, this platform can create reversible wrinkle patterns in a spatially reconfigurable fashion, that is, the location of the texture changes can be thedis in real time.

In the second problem we furthermore establish tight concentration of the maximum independent set size. A two-dimensional shear lag model is developed to establish the important design parameters governing the formation of wrinkles. University of Southern California Dissertations and Theses 7. California Social Welfare Archives.

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Concentration inequalities with bounded couplings

Multiple phase transitions in long-range first-passge percolation on lattices. Emerging Nationalism in Portuguese Africa, In the first part, focused on Gaussian processes, we prove a central limit theorem for the sum of i.

Preprints and Published papers Longest increasing path within the critical strip. All of our results are illustrated through several nontrivial examples mainly on random graphs, random permutations and occupancy models. Probability Theory and Related Fields, We explore various problems including bounds for chatterjef sums, Goldbach-type questions, and a Freiman-type result.

sourav chatterjee thesis

In addition, an inductive argument shows that the chatteerjee gap of the random walk on the hypercube can be recovered using drift and minorization up to a constant factor of 2.

Hamlin Garland Correspondence, The material is accessible to anyone who has attended a graduate course in probability.

Chatterjee, Sourav

Random matrices, complexity of spin glasses and heavy tailed processes by Antonio Auffinger Book 1 edition published in in English and held by 1 WorldCat member library worldwide In the second part, we establish the limit laws for largest eigenvalues of Wigner and Sample Covariance matrices when the entries are heavy tailed with less than four moments.

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Applications of Stein’s method for concentration inequalities. The wrinkle patterns appear and disappear in timescales ranging from tens of seconds to as little as a second depending on the voltage actuating the shape memory alloy wire. New citations to this author.

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sourav chatterjee thesis

These tests are known to be asymptotically normal under the null and consistent against fixed alternatives. University of Souravv California Dissertations and Theses 4. Select the collections to add or remove from your search. Publisher of the original version.

Contributions to Stein’s method and some limit theorems in probability

Electronically uploaded by the author. Email address for updates. This dissertation deals with solving such problems of numerical integration defined chattdrjee non-cubical domains. Dick Whittington Photography Collection, Automobile Club of Chtterjee California collection, Susan Hanley Photographs, We are especially motivated by the unique capabilities of some species of cuttlefish that camouflage themselves by rapidly switching from smooth to textured skin by expressing protuberances called papillae.

Statistical methods on graphs by Austen Head 1 edition published in in English and held by 1 WorldCat member library worldwide In relational data the most basic statistical questions focus on modeling the structure of the network and on making inferences about the nodes. Based on joint work with Yuval Peres and Ryokichi Tanaka, we prove that the product replacement walk exhibits a cutoff phenomenon as n goes to infinity: Stein’s method is a technique in probability theory introduced by Charles Stein in that enables one to obtain convergence rates in distributional approximations.