Oberseminar Wahrscheinlichkeitstheorie
Joint research seminar of LMU and TUM in Probability Theory
Students and guests welcome.
Organizers:
Noam
Berger (TUM),
Nina
Gantert
(TUM),
Konstantinos Panagiotou (LMU),
Markus
Heydenreich (LMU),
Sabine
Jansen (LMU),
Franz Merkl
(LMU),
Silke
Rolles (TUM)
Upcoming talks:
| Mon 11 May 2026, 16:30: Léo Daures Large deviations for reducible Markov chains |
| Let $ (X_n)$ be a Markov chain and let $L_n$ denote its empirical measure at time $n$. We are interested in the large deviations of $(L_n)$. Roughly speaking, proving a large deviation principle for $(L_n)$ means proving that, for any given measure $\mu$, the probability of $L_n$ being close to $\mu$ decays with $n$ at an exponential rate (depending on $\mu$). The large deviations of $(L_n)$ have been studied since the 1970s and are well understood in "good" cases, in particular under assumptions of irreducibility of the Markov chain. However, very some simple Markov chains fail to satisfy these irreducibility assumptions. It turns out that transient states may play a role in large deviations, and complex behaviours can emerge at the large deviations scale when the Markov chain is not irreducible. I will describe these behaviours and present a new method for deriving the weak large deviation principle for $(L_n)$ in the reducible case, despite the resulting complication. |
| Parkring 11, Garching-Hochbrück. Room BC1 2.01.10 (8101.02.110) |
| Mon 18 May 2026, 16:30: Alan Sergeev Majority Dynamics on Graphs |
| Given a simple graph G = (V, E) and a map l0 : V → {+1, −1}, the majority dynamics on G with initial assignment of states l0 is a process that begins on day 0, and for each t ≥ 0 produces a new assignment of states lt+1 where each vertex takes the state of the majority of its neighbours, and remains at its previous state in the case of a tie. Specifically, for each v ∈ V , lt+1(v) = ( +1 if P u∈N (v) lt(u) > 0, or P u∈N (v) lt(u) = 0 and lt(v) = +1, −1 otherwise. (1) This process is a model for opinion exchange dynamics, with applications in many areas, such as politics, sociology, biophysics. While there exist results about the process even- tually reaching a 2-periodic stable state on all graphs, a natural question to study would be under which initial conditions is unanimity reached, and how quickly. When considering the question specifically in the case of Binomial Random Graphs, a longstanding conjecture, due to Benjamini, Chan, O’Donnel, Tamuz and Tan (2016) is the following: Conjecture. Let G ∼ G(n, p) be the binomial random graph with p = ω(1/n) and l0(v) be sampled uniformly at random from {+1, −1} for each v ∈ V . Then w.h.p. the majority dynamics process reaches unanimity after sufficiently many steps t. Steps towards proving the conjecture have been taken taken by gradually improving the range densities d = np for which the conjecture is known to be true, with the current best bound being d ≫ n1/3 log2/3 n due to Kim and Tran. Our work aims to prove the conjecture for the range n1/4 ≪ d ≤ O(n1/3), and lays the groundwork for proving the conjecture in the general case n1/(k+1) ≪ d ≤ O(n1/k). This is based on joint work with Nikolaos Fountoulakis, University of Birmingham. |
| Theresienstr. 39, Theresienstr. 39. Room B 252 |
| Mon 1 Jun 2026, 15:30: Vitali Wachtel TBA |
| TBA |
| Parkring 11, Garching-Hochbrück. Room BC1 2.01.10 (8101.02.110) |
| Mon 1 Jun 2026, 17:00: Dieter Mitsche On the mixing time of random geometric graphs |
| We study the mixing time of the simple random walk on the giant component of supercritical $d$-dimensional random geometric graphs generated by the unit intensity Poisson Point Process in a $d$-dimensional cube of volume $n$. With $r_g$ denoting the threshold for having a giant component, we show that for every $\epsilon>0$ and any $r\geq(1+\epsilon)r_g$, the mixing time of the giant component is with high probability $\Theta(n^{2/d}/r^2)$, thereby closing a gap in the literature. Our analysis also implies that the relaxation time is of the same order. Joint work with M. Kiwi and C. Martinez. |
| Parkring 11, Garching-Hochbrück. Room BC1 2.01.10 (8101.02.110) |
| Mon 8 Jun 2026, 16:30: Adrien Malacan TBA |
| TBA |
| Parkring 11, Garching-Hochbrück. |
| Tue 9 Jun 2026, 16:00: Jakob Maier TBA |
| TBA |
| Parkring 11, Garching-Hochbrück. Room BC1 2.01.10 (8101.02.110) |