“Between grief and nothing I will take grief.” ― William Faulkner

Personal Interests

I am a cinephile, enjoying watching a variety of films. When I’m not immersed in mathematics, I spend lots of my free time watching movies. My all-time favorite director is Karwei Wong, who first inspired my love for movies. I have great admiration for the works of Stanley Kubrick as well, who is an absolute genius. In fact, I have a dream to be a director. My Douban page is here.

Also, I appreciate the works from Tatsuki Fujimoto (藤本树) very much although I don’t often read manga.

The following are my TOP 15:

• Burning (2018), directed by Lee Chang-dong

• Swallowtail Butterfly (1996), directed by Shunji Iwai

• The Curious Case of Benjamin Button (2008), directed by David Fincher

• Fight Club (1999), directed by David Fincher

• Taxi Driver (1976), directed by Martin Scorsese

• Days of Being Wild (1990), directed by Karwei Wong

• Blue Velvet (1986), directed by David Lynch

• American Psycho (2000), directed by Mary Harron

• Thirst (2009), directed by Park Chan-wook

• Fallen Angels (1995), directed by Karwei Wong

• Interstellar (2014), directed by Christopher Nolan

• Eyes Wide Shut (1999), directed by Stanley Kubrick

• Being John Malkovich (1999), directed by Spike Jonze

• Black Swan (2010), directed by Darren Aronofsky

• New World (2013), directed by Park Hoon-jung

• Drive My Car (2021), directed by Ryusuke Hamaguchi

• Three Colours: Red (1994), directed by Krzysztof Kieślowski

My top two favorite series are:

• Breaking Bad

• Better Call Saul

Interesting Quizzes

Q1: For two sequence of r.v.’s (Xn) and (Yn) independent in a same probability space. If Xn→X,Yn→Y both in distribution. Do you think Xn+Yn→X+Y in distribution?

Think it carefully. You can modify the statement and make it more tricky.

Q2: How to prove any two families of o.n.b of one Hilbert space have the same cardinality?

You will find sth amazing in definition of “SUM”.

Q3: Do you really think p(θ∈(a,b))∈{0,1} for some parameter θ?

This is an essential difference between a Bayesian and a Frequenist.

Q4: For a given r.v. X, could you find a r.v. Y st. it’s i.i.d. as X?

Generally, we require the probability space to be nonatomic to guaratee the indepedence will hold. And You can search for a THM called Skorokhod’s Representation THM, which is one of my most favourite THM in Probability.

Q5: For a n.v.s E. Assume F is a close subspace of E, is there a m in F st. d(x,F)=d(x,m)?

There’s a sufficient and necessary condition for its holding.

Q6: Do you think one transition function can correspond one CTMC? What’s about one generator and one CTMC?

It first amazes me because it’s a simple example that satisfies strong Markov property but not a Feller process. (Actually, Feller property is a stronger property than merely strong Markov) If you are interested in this question, you can search for a process called Blackwell process.

Q7: What’s the dual space of R^∞ equipped with box topology?

Can you recall the definition of dual space? You can think it algebracally rather than analysisly.(hint: search for concepts: inductive limit and projective limit).