# Schedule for: 19w2282 - Retreat for Young Researchers in Probability and areas of Application

Arriving in Banff, Alberta on Friday, September 27 and departing Sunday September 29, 2019

Friday, September 27 | |
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16:00 - 19:30 |
Check-in begins (Front Desk – Professional Development Centre - open 24 hours) ↓ Note: the Lecture rooms are available after 16:00. (Front Desk – Professional Development Centre) |

19:30 - 22:00 |
Informal gathering in 2nd floor lounge, Corbett Hall ↓ Beverages and a small assortment of snacks are available in the lounge on a cash honour system. (TCPL or Corbett Hall Lounge (CH 2110)) |

Saturday, September 28 | |
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07:00 - 09:00 |
Breakfast ↓ A buffet breakfast is served daily between 7:00am and 9:00am in the Vistas Dining Room, the top floor of the Sally Borden Building. Note that BIRS does not pay for meals for 2-day workshops. (Vistas Dining Room) |

08:45 - 09:00 |
Welcome Talk by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |

09:00 - 09:40 |
Zhongwei Shen: A quasi-stationary distribution approach to transient dynamics [Chair: Ed Perkins] ↓ Transient dynamics, often observed in multi-scale systems,
are roughly defined to be the interesting dynamical behaviors that
display over finite time periods. For a class of randomly perturbed
dynamical systems that arise in chemical reactions and population
dynamics, and that exhibit persistence dynamics over finite time
periods and extinction dynamics in the long run, we use
quasi-stationary distributions (QSDs) to rigorously capture the
transient states governing the transient dynamics. We study the
noise-vanishing concentration of the QSDs to gain information about the
transient states. (TCPL 201) |

09:45 - 10:25 |
Joseph Horan: A cocycle Perron-Frobenius theorem for random dynamical systems on Banach spaces ↓ The classical Perron-Frobenius theorem can be applied to Markov
chains with a single primitive transition matrix to show that there is a unique
stationary distribution for the chain, and that distributions relax
exponentially quickly to that stationary distribution, where the rate is
determined by the second-largest eigenvalue. We can generalize Markov chains:
first to chains with randomly chosen transition matrices, then to cocycles of
transfer operators, which describe how densities move around according to
random underlying dynamics on a state space. I will describe a generalization
of the classical Perron-Frobenius theorem that can be applied in this setting
to give an analog of a stationary distribution and a relaxation rate, along
with some of the definitions and background required to understand the theorem
statement. (TCPL 201) |

10:30 - 10:50 | Coffee Break (TCPL Foyer) |

10:50 - 11:30 |
Delphin Sénizergues: Asymptotic properties of weighted recursive and preferential attachment trees [Chair:Gourab Ray] ↓ Starting from a sequence of positive real numbers (w_n),
which we call weights, we construct a tree in a recursive manner: at
time 1, the tree has only one vertex. Then at any step n+1, we add a
new vertex to the tree and we choose its parent at random among the
already existing vertices, in such a way that the k-th vertex (in order
of creation) is chosen with probability proportional to w_k.
This model generalises the well-known uniform recursive tree (URT) in
the case of a constant sequence (w_n). In fact, it can also be shown
that the trees constructed using affine preferential attachment can be
described with this construction, using a random sequence of weights
(w_n).
We prove almost-sure scaling limits for the height, profile and degrees
in the tree as the number of vertices tends to infinity. These results
are related to proving scaling limits in the Gromov-Hausdorff-Prokhorov
topology for a family of random growth models on graphs that
generalises Rémy's algorithm. (TCPL 201) |

11:35 - 12:15 |
Josh Rosenberg: The Poisson frog model on Galton-Watson trees ↓ We consider an interacting particle system on trees known as
the frog model: initially, a single active particle begins at the root
and i.i.d. Poisson(u) many inactive particles are placed at each
non-root vertex. Active particles perform discrete time simple random
walk and activate the inactive particles they encounter. It has been
shown by Hoffman, Johnson, and Junge that on regular trees, there is a
critical value uc separating recurrent and transient regimes. Little
is known, however, about the behavior of the frog model on random
structures, and other graphs that do not posses a high degree of
self-similarity. In this talk, I'll discuss our recent results showing
that for Galton-Watson trees with certain types of offspring
distributions there does exist a critical value uc separating recurrent
and transient regimes for almost surely every tree, thereby partially
answering a question of Hoffman-Johnson-Junge. I'll also discuss a
related proof showing that for every non-amenable tree with bounded
degree there exists a phase transition from transience to recurrence
(with a non-trivial intermediate phase sometimes sandwiched in between)
as u varies. This is based on joint work with Marcus Michelen. (TCPL 201) |

12:20 - 12:35 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |

12:35 - 13:30 |
Lunch ↓ A buffet lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. Note that BIRS does not pay for meals for 2-day workshops. (Vistas Dining Room) |

13:45 - 14:25 |
Chandra Rajulapati: Stochastic modelling of extreme precipitation-from global scale to urban scale [Chair:Yaozhong Hu] ↓ Extreme precipitation, driven by complex spatiotemporal
processes, is characterized by limited predictability. Modeling
precipitation extremes and understanding their spatial and temporal
variations are important for long-term planning. The talk focuses on
describing stochastic methods to model extremes at global and regional
scale. The global picture of how precipitation properties vary across
time and space, specifically in regions where ground-based
observations are scarce, is discussed. Uncertainties, quantified using
Bayesian techniques, in modelling extremes are enumerated. Importance
of studying the uncertainties and propagating them to future for
accurate assessment of projected precipitation is emphasized. (TCPL 201) |

14:30 - 14:50 | Coffee Break (TCPL Foyer) |

14:50 - 15:30 |
Wenning Wei: Optimal Liquidation in Target Zone Models and Neumann Problem of Backward SPDEs with Singular Terminal Condition ↓ We study the optimal liquidation problems in target zone models with
dynamic programming methods. Such control problems allow for stochastic
differential equations with reflections and random coefficients. The
value function is characterized by a Neumann problem of backward
stochastic partial differential equations (BSPDEs) with singular
terminal conditions. The existence and the uniqueness of strong
solution to such BSPDEs are addressed, which in turn yields the optimal
feedback control. (TCPL 201) |

15:35 - 16:35 | Open Problems Session [Chair: Chris Hoffman] (TCPL 201) |

16:35 - 18:35 | Hike to Tunnel Mountain, Bow River, Free Time (TCPL 201) |

17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. Note that BIRS does not pay for meals for 2-day workshops. (Vistas Dining Room) |

Sunday, September 29 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:40 |
Shirou Wang: Desynchronization for Markov perturbation of synchronized random networks [Chair: Yingfei Yi] ↓ A physical network is naturally subject to noise influences
from both external (extrinsic) and internal (intrinsic) sources. The
extrinsic noises are usually environmentally related, while the
intrinsic ones are typically due to internal uncertainties. A
discrete-time, discrete-state (dtds) network with only extrinsic noises
is commonly modeled by a discrete random dynamical system (RDS), but
the one with only intrinsic noises is often modeled by a Markov chain.
In this talk, we will consider a dtds network with both extrinsic and
intrinsic noises under the framework of the so-called Markov random
network (MRN). In particular, we will discuss the phenomenon and
mechanism of desynchronizations for MRNs which arise as
Markov-perturbations of a synchronized discrete RDS. Characterization
of desynchronizations will be given from the view points of both
probability distributions and dynamical systems. This is an ongoing
joint work with Profs. Arno Berger, Hong Qian, and Yingfei Yi. (TCPL 201) |

09:45 - 10:25 |
Weiwei Qi: On time-periodic Fokker-Planck equations ↓ In this talk, we will study time-periodic Fokker-Planck
equation (FPE) which arise from stochastic differential equations with
time-periodic coefficients, including the existence and uniqueness of
periodic probability solutions to FPE, and convergence of global
probability solutions of the associated Cauchy problem of FPE. As an
application, the long-time behavior of a stochastic damping Hamiltonian
system is investigated. (TCPL 201) |

10:30 - 11:50 |
Checkout by Noon ↓ 2-day workshop participants are welcome to use BIRS facilities (Corbett Hall Lounge, TCPL, Reading Room) until 15:00 on Sunday, although participants are still required to checkout of the guest rooms by 12 noon. There is no coffee break service on Sunday afternoon, but self-serve coffee and tea are always available in the 2nd floor lounge, Corbett Hall. (Front Desk – Professional Development Centre) |

10:30 - 10:50 | Coffee Break (TCPL Foyer) |

10:50 - 11:30 |
Thomas Budzinski: Random (non-planar) maps with unconstrained genus [Chair: Martin Barlow] ↓ We study random gluings of polygons where the genus is not fixed
a priori. We will study the law of the degrees of thee largest vertices
and show that they are described by a Poisson-Dirichlet process. We use
probabilistic arguments, which contrasts sharply with the algebraic tools
usually used to prove similar results. Based on joint work with Nicolas
Curien and Bram Petri. (TCPL 201) |

11:35 - 12:15 |
Yinon Spinka: Infinite random geometric graphs on a circle ↓ Let $(X,d)$ be a metric space and let V be a dense
countable subset of X. Construct a random graph G on V by placing
an edge between any two points in V with probability q if the
distance between them is less than one (and do so independently
for different pairs of points). We are interested in the
almost-sure properties of G, or more specifically, of the
isomorphism class of G. Such properties may be very sensitive to
the metric space (though usually less to V and q). For example,
Bonata and Janssen, who initiated the study of these graphs,
showed that in the case of the $(R^d,L_\infty)$, two independent
samples of G are almost surely isomorphic, whereas in the case of
$(R^d,L_p)$ with $1 $<$p<\infty$ (including the Euclidean case $p=2$), two
such samples are almost surely non-isomorphic. We consider the
case of a circle R/LZ of length L with its intrinsic metric, and
show a surprising dependence of behavior on L. Joint with Omer Angel. (TCPL 201) |

12:20 - 13:30 | Lunch in Vistas (Vistas Dining Room) |