DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272017-07-09T00:28:33Z2017-07-09T00:28:33ZInviscid traveling waves of monostable nonlinearityChoi, Sun-HoChung, JaywanKim, Yong-Junghttp://hdl.handle.net/10203/2240202017-06-16T03:56:22Z2017-09-01T00:00:00ZTitle: Inviscid traveling waves of monostable nonlinearity
Authors: Choi, Sun-Ho; Chung, Jaywan; Kim, Yong-Jung
Abstract: Inviscid traveling waves are ghost-like phenomena that do not appear in reality because of their instability. However, they are the reason for the complexity of the traveling wave theory of reaction diffusion equations and understanding them will help to resolve related puzzles. In this article, we obtain the existence, the uniqueness and the regularity of inviscid traveling waves under a general monostable nonlinearity that includes non-Lipschitz continuous reaction terms. Solution structures are obtained such as the thickness of the tail and the free boundaries. (C) 2017 Elsevier Ltd. All rights reserved.2017-09-01T00:00:00ZLocal universal lifting spaces of mod l Galois representationsChoi, Suh Hyunhttp://hdl.handle.net/10203/2234042017-06-29T06:05:16Z2017-07-01T00:00:00ZTitle: Local universal lifting spaces of mod l Galois representations
Authors: Choi, Suh Hyun
Abstract: Let p and l be distinct primes, K a finite extension of Q(p), and (rho) over bar : Gal((K) over bar /K)-> GL(n),((F) over barl) a mod l Galois representation. In this paper, we show that the generic fiber of universal lifting space of (rho) over bar is equidimensional of dimension n(2). We also characterize the irreducible components of the generic fiber of the universal lifting space which represent the liftings rho's of (rho) over bar with unipotent rho vertical bar I-K's, when pi', is trivial or n <= 4 and the square of the order of the residue field of K is not equal to 1 mod l. (C) 2017 Elsevier Inc. All rights reserved.2017-07-01T00:00:00ZCOLORFUL THEOREMS FOR STRONG CONVEXITYHolmsen, Andreas F.Karasev, Romanhttp://hdl.handle.net/10203/2236432017-05-15T05:16:51Z2017-06-01T00:00:00ZTitle: COLORFUL THEOREMS FOR STRONG CONVEXITY
Authors: Holmsen, Andreas F.; Karasev, Roman
Abstract: We prove two colorful Caratheodory theorems for strongly convex hulls, generalizing the colorful Caratheodory theorem for ordinary convexity by Imre Barany, the non-colorful Caratheodory theorem for strongly convex hulls by the second author, and the "very colorful theorems" by the first author and others. We also investigate if the assumption of a "generating convex set" is really needed in such results and try to give a topological criterion for one convex body to be a Minkowski summand of another.2017-06-01T00:00:00ZFluctuations of the Free Energy of the Spherical Sherrington-Kirkpatrick Model with Ferromagnetic InteractionBaik, JinhoLee, Ji Oonhttp://hdl.handle.net/10203/2240492017-06-20T02:00:50Z2017-06-01T00:00:00ZTitle: Fluctuations of the Free Energy of the Spherical Sherrington-Kirkpatrick Model with Ferromagnetic Interaction
Authors: Baik, Jinho; Lee, Ji Oon
Abstract: We consider a spherical spin system with pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction. The system shows a two-dimensional phase transition with respect to the temperature and the coupling constant. We compute the limiting distributions of the free energy for all parameters away from the critical values. The zero temperature case corresponds to the well-known phase transition of the largest eigenvalue of a rank 1 spiked random symmetric matrix. As an intermediate step, we establish a central limit theorem for the linear statistics of rank 1 spiked random symmetric matrices.2017-06-01T00:00:00Z