Titles & Abstracts

Title: Gibbs measures on subshifts

Abstract: We consider some of the main notions of Gibbs measures on subshifts introduced by different communities, such as dynamical systems, probability, operator algebras, and mathematical physics. For potentials with d-summable variation, we prove that several of the definitions considered by these communities are equivalent. In particular, when the subshift is of finite type (SFT), we show that all definitions coincide. In addition, we introduced a groupoid approach to describe some Gibbs measures, allowing us to show the equivalence between Gibbs measures and KMS states (the quantum analog of the Gibbs measures).  

Title: The FKG inequality for contact process in an evolving random environment and its applications

Abstract: The contact process with dynamic edges (CPDE) is a model for the spread of infection in which the state of each edge transmitting infection, available or unavailable, switches randomly over time.

It is well known that the FKG inequality holds for the time-homogeneous contact process. This inequality is one of the most important tools for analyzing the properties of the process.

In this talk, I will prove that the FKG inequality also holds for the CPDE. In addition, based on this result, I will present a hyperscaling inequality and show that the critical CPDE dies out.

Title: Spectral analysis of q-deformed unitary ensembles with the Al-Salam-Carlitz weight

Abstract: Al-Salam–Carlitz polynomial is a family of basic hypergeometric orthogonal polynomials in the Askey Scheme, which arises in a natural generalization of q-deformed Gaussian unitary ensemble. In this talk, I will first introduce Flajolet and Viennot’s theory concerning the combinatorics of the spectral moments of orthogonal polynomials, which yields a sign-definite sum formula of spectral moments. This leads to an explicit description of the limiting spectral density. This talk is based on joint work with Sung-Soo Byun and Jaeseong Oh.

Title: Reverse data-processing inequalities for partial transposes of random quantum states

Abstract: The quantum data processing inequality (QDPI) states that quantum relative entropy cannot be increased by local physical operations. However, the partial transposition can be used to increase the quantum relative entropy on random quantum states with probability one. We explain why such an unexpected phenomenon happens in view of random matrix theory and free probability.