A Topologically Mixing 2 Dimensional Infinite Particles System

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

On (2+1)Dimensional Topologically Massive Non-linear Electrodynamics

The (2+1) dimensional non-linear electrodynamics, the so called Pagels–Tomboulis electrodynamics, with the Chern–Simons term is considered. We obtain ”generalized self–dual equation” and find the corresponding generalized massive Chern–Simons Lagrangian. Similar results for (2+1) massive dilaton electrodynamics have been obtained. 1 The Pagels–Tomboulis model Among many gauge theories the Pagel...

On infinite-volume mixing

In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinitevolume average. The idea is borrowed from statistical mechanics and appears to be relevant, at least for extended systems with a direct physical interpretation. We discuss the pros and cons of a few mathematical definitions that can be devised, te...

Topologically-Protected Low Dimensional Metals

Mixing of diffusing particles.

We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial configuration. In the steady state, the distribution of the inversion number is Gaussian with the average ≃ N²/4 and the standard deviation σ ≃ N³/²/6. The survi...