This website uses features that are not well-supported by your browser. Please consider upgrading to a browser and version that fully supports CSS Grid and the CSS Flexible Box Layout Module.

Our commitment to inclusivity

Diversity and inclusivity are necessary partners. Without inclusivity, the benefits of diversity — an increase in understanding, improvement in performance, enhanced innovation, and heightened levels of satisfaction — will not be realized. We commit to investments in both, to create a community in which difference is valued, where each individual’s identity and contributions are treated with respect, and where differences lead to a strengthened identity for all. See Dartmouth College Inclusive Excellence Action Plan and Arts and Sciences Inclusive Excellence Reports.

Texas Tech University

007 Kemeny Hall, 4 pm

Tea 3:30 pm, 300 Kemeny Hall

**Abstract: **
We have extensively studied the systems $$\dot{x}=(\delta(t)A+(1-\delta(t))B)x(t),\ \ \delta(t)\in\{0,1\}$$, \begin{eqnarray*}dx&=&(z(t)A+(1-z(t))B)dt\\dz&=&(1-2z)dN_\lambda\end{eqnarray*} and $$x_{n+1}=(\delta_1A_1+\cdots+\delta_kA_k)x_n$$ where $\delta_i\in\{0,1\}$, $\delta_1+\cdots+\delta_k=1$ and $P(\delta_i=1)=p_i$ and we have a fairly good understanding of when these systems are stable. Our interest has now moved to an attempt to understand what happens when they are not stable. Interesting phenomena occurs when we consider a representation of a finite group $G$, i.e. a homomorphism, $L$, from $G$ into $Hom(V,V)$.We now consider the system $$X_{n+1}=(\delta_1L(g_1)+\cdots+\delta_kL(g_k))xX_n$$ where $\delta_i\in\{0,1\}$, $\delta_1+\cdots+\delta_k=1$, $P(\delta_i=1)=p_i$ and $X_0=I$. Because $X_n=L(g)$ for some $g\in G$ the system evolves on the image of the representation. Using linear system theory we can calculate all of the moments of the limiting distribution and using the fact that the system creates a Markov process we can calculate the transition probability matrix. A nice interplay between systems theory and the work of Perci Diaconis on the role of groups in probability and statistics develops. The results have applications in such diverse areas as magic and genetics.

This talk will be accessible to graduate students.