标题： Liouville量子对偶性与随机平面图 显示英文标题

标题： Liouville Quantum Duality and Random Planar Maps

摘要： 我们考虑块加权随机平面图模型，在这些模型中，可能装饰的图被规范地分解为块，每个块获得权重$u$。 这些图在某个临界值$u=u_{cr}$处出现相变，超过该值后，图退化为布朗树。 我们证明了在$u=u_{cr}$处的图的计数性质和临界指数与$u<u_{cr}$处的那些之间存在由对偶关系连接，这些对偶关系正是在随机曲面的Liouville量子引力描述背景下所预期的。 我们通过各种块加权图的例子来说明这一结果：分解为简单块的随机平面四边形图，分解为不可约块的三次或双三次平面图上的哈密顿圈，以及测地线系统。 显示英文摘要

摘要： We consider models of block-weighted random planar maps in which possibly decorated maps are decomposed canonically into blocks, each block receiving the weight $u$. These maps present a transition at some critical value $u=u_{cr}$ above which the maps degenerate into Brownian trees. We show that the enumerative properties and critical exponents of the maps at $u=u_{cr}$ and those for $u<u_{cr}$ are connected by duality relations which are precisely those expected in the context of the Liouville quantum gravity description of random surfaces. We illustrate this result by various instances of block-weighted maps: random planar quadrangulations decomposed into simple blocks, Hamiltonian cycles on cubic or bicubic planar maps decomposed into irreducible blocks, and meandric systems.