All¹ X11 programs open their windows on the display indicated by the environment variable DISPLAY. Thus:
sudo -u 1000 env DISPLAY=:0 xev
or for that matter, since you can run programs as a different user from the X server, just
DISPLAY=:0 xev
:NUMBER is the notation for local displays; in most scenarios, the X11 server that is running on the console is the one that's started first and ends up being number 0. You can run echo "$DISPLAY" in a terminal on that display to check whether the display number is correct. :0.0 is equivalent to :0 (a trailing .0 can be omitted).
If you run the program as a different user from the X server, and sometimes even if you run it as the same user, you may need to set the XAUTHORITY environment variable as well. This variable points to a file that contains a password (called a cookie) that applications must pass to the X server. To see the right value from XAUTHORITY, run echo $XAUTHORITY on that display; if it's unset, the default value is ~/.Xauthority where ~ represents the user's home directory.
If you need to find the values of DISPLAY and XAUTHORITY programmatically, see Open a window on a remote X display (why "Cannot open display")?
¹ At least almost all. It's technically possible for them not to, but it takes active work on the part of the programmer to make it not so, whereas a -display argument is a convention that is far from universal.
DISPLAY. For Display0you can doDISPLAY=:0 xev. Now you will get an error about security X11 has security to stop you doing this. You need to look intoxauth. Notexhost +is dangerous. – ctrl-alt-delor Feb 19 '15 at 22:51