اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn interacting particle model and a Pieri-type formula for the orthogonal group
118
0
0.0
(
0
)
تأليف
Manon Defosseux
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We introduce a new interacting particles model with blocking and pushing interactions. Particles evolve on the positive line jumping on their own volition rightwards or leftwards according to geometric jumps with parameter q. We show that the model involves a Pieri-type formula for the orthogonal group. We prove that the two extreme cases - q=0 and q=1 - lead respectively to a random tiling model studied by Borodin and Kuan and to a random matrix model.
قيم البحث
اقرأ أيضاً
We have introduced recently a particles model with blocking and pushing interactions which is related to a Pieri type formula for the orthogonal group. This model has a symplectic version presented here.
The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for the Skorokhod map $Gamma_{0,a}$ on $[0,a]$ for any $a>0$ is derived. Spe
cifically, it is shown that on the space $mathcal{D}[0,infty)$ of right-continuous functions with left limits taking values in $mathbb{R}$, $Gamma_{0,a}=Lambda_acirc Gamma_0$, where $Lambda_a:mathcal{D}[0,infty)tomathcal{D}[0,infty)$ is defined by [Lambda_a(phi)(t)=phi(t)-sup_{sin[0,t]}biggl[bigl( phi(s)-abigr)^+wedgeinf_{uin[s,t]}phi(u)biggr]] and $Gamma_0:mathcal{D}[0,infty)tomathcal{D}[0,infty)$ is the Skorokhod map on $[0,infty)$, which is given explicitly by [Gamma_0(psi)(t)=psi(t)+sup_{sin[0,t]}[-psi(s)]^+.] In addition, properties of $Lambda_a$ are developed and comparison properties of $Gamma_{0,a}$ are established.
We study the spectrum reconstruction technique. As is known to all, eigenvalues play an important role in many research fields and are foundation to many practical techniques such like PCA(Principal Component Analysis). We believe that related algori
thms should perform better with more accurate spectrum estimation. There was an approximation formula proposed, however, they didnt give any proof. In our research, we show why the formula works. And when both number of features and dimension of space go to infinity, we find the order of error for the approximation formula, which is related to a constant $c$-the ratio of dimension of space and number of features.
Elaborating on the model from voter process with mixed-mechanism under suitable scaling, I have two new mechanisms which are random switch and unbiased local Homogenization and subtly biased advantage but with state dependent coefficient involved. Th
e most crucial one, the existence of high-frequency duplication generating the diffusion term and noise term in each case identifies the limit equation as SPDE driven by space time white noise.
We provide a new tableau model from which one can easily deduce the characters of irreducible polynomial representations of the orthogonal group $mathrm{O}_n(mathbb{C})$. This model originates from representation theory of the $imath$quantum group of
type AI, and is equipped with a combinatorial structure, which we call AI-crystal structure. This structure enables us to describe combinatorially the tensor product of an $mathrm{O}_n(mathbb{C})$-module and a $mathrm{GL}_n(mathbb{C})$-module, and the branching from $mathrm{GL}_n(mathbb{C})$ to $mathrm{O}_n(mathbb{C})$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
